{"id":41028,"date":"2024-09-25T11:28:10","date_gmt":"2024-09-25T11:28:10","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%87%d9%85%d9%88%d8%a7%d8%b1%d8%b3%d8%a7%d8%b2%db%8c-%d9%be%d8%b1%d9%88%d8%ac%da%a9%d8%aa%db%8c%d9%88\/"},"modified":"2024-09-25T11:29:30","modified_gmt":"2024-09-25T11:29:30","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%87%d9%85%d9%88%d8%a7%d8%b1%d8%b3%d8%a7%d8%b2%db%8c-%d9%be%d8%b1%d9%88%d8%ac%da%a9%d8%aa%db%8c%d9%88","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%87%d9%85%d9%88%d8%a7%d8%b1%d8%b3%d8%a7%d8%b2%db%8c-%d9%be%d8%b1%d9%88%d8%ac%da%a9%d8%aa%db%8c%d9%88\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0647\u0645\u0648\u0627\u0631\u0633\u0627\u0632\u06cc \u067e\u0631\u0648\u062c\u06a9\u062a\u06cc\u0648 \u0627\u0646\u0648\u0627\u0639 \u0628\u0627 \u062a\u0642\u0627\u0637\u0639 \u0647\u0627\u06cc \u0645\u0639\u0645\u0648\u0644\u06cc \u0633\u0627\u062f\u0647"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nProjective smoothing of varieties with simple normal crossings<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0647\u0645\u0648\u0627\u0631\u0633\u0627\u0632\u06cc \u067e\u0631\u0648\u062c\u06a9\u062a\u06cc\u0648 \u0627\u0646\u0648\u0627\u0639 \u0628\u0627 \u062a\u0642\u0627\u0637\u0639 \u0647\u0627\u06cc \u0645\u0639\u0645\u0648\u0644\u06cc \u0633\u0627\u062f\u0647<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nPurnaprajna Bangere, Francisco Javier Gallego, Jayan Mukherjee<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n29<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nAlgebraic Geometry,\u0647\u0646\u062f\u0633\u0647 \u062c\u0628\u0631\u06cc ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 6 March, 2024; originally announced March 2024. , Comments: 29 pages, Comments are welcome ! , MSC Class: 14B05; 14B10; 14D06; 14D15; 14D20; 14E30; 14J10; 14J45<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 6 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u0646\u0638\u0631\u0627\u062a: 29 \u0635\u0641\u062d\u0647 \u060c \u0646\u0638\u0631\u0627\u062a \u062e\u0648\u0634 \u0622\u0645\u062f\u06cc\u062f!\u060c \u06a9\u0644\u0627\u0633 MSC: 14B05 \u061b14B10 \u061b14d06 \u061b14d15 \u061b14d20 \u061b14e30 \u061b14J10 \u061b14J45<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

In this article, we introduce a new approach to show the existence and smoothing of simple normal crossing varieties in a given projective space. Our approach relates the above to the existence of nowhere reduced schemes called ribbons and their smoothings via deformation theory of morphisms. As a consequence, we prove results on the existence and smoothing of snc subvarieties $V \\subset \\mathbb{P}^N$, with two irreducible components, each of which are Fano varieties of dimension $n>2$, embedded inside $\\mathbb{P}^{N}$ for effective values of $N$, by the complete linear series of a line bundle $H$. The general fibers of the resulting one parameter families are either smooth Fano, Calabi-Yau or varieties of general type, depending on the positivity of the canonical divisor of their intersections. An interesting consequence of projective smoothing is that it automatically gives a smoothing of the semi-log-canonical (slc) pair $(V, \u0394)$, where $\u0394= cH$, $c < 1$, is a rational multiple of a general hyperplane section of $H$. For threefolds, we are able to give explicit descriptions of the smoothable snc subvarieties due to the classification results of Iskovskikh-Mori-Mukai. In particular, we show the existence of unions V = $Y_1 \\bigcup_D Y_2 \\subset \\mathbb{P}^N$, where $Y_i$'s are smooth anticanonically (resp. bi-anticanonically) embedded Fano threefolds, intersecting along $D$, where $D$ is either a del-Pezzo surface or a $K3$ surface (resp. a smooth surface with ample canonical bundle) and their smoothing in $\\mathbb{P}^N$ to smooth Fano or Calabi-Yau threefolds (resp. to threefolds with ample canonical bundle) for various values of $N$ between $10$ and $163$. In cases when the general fiber is a smooth Fano or Calabi-Yau threefold, one can choose $c$ such that $(V, \u0394)$ is a Calabi-Yau pair while in all cases $c$ can be chosen so that $(V, \u0394)$ is a stable pair.<\/p>\n

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\u06cc\u0627 \u0627\u0646\u0648\u0627\u0639 \u0645\u062e\u062a\u0644\u0641\u06cc \u0647\u0633\u062a\u0646\u062f.\u06cc\u06a9 \u0646\u062a\u06cc\u062c\u0647 \u062c\u0627\u0644\u0628 \u0627\u0632 \u0647\u0645\u0648\u0627\u0631 \u0633\u0627\u0632\u06cc \u067e\u0631\u0648\u0698\u06a9\u062a\u0648\u0631 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0637\u0648\u0631 \u062e\u0648\u062f\u06a9\u0627\u0631 \u06cc\u06a9 \u0647\u0645\u0648\u0627\u0631 \u0633\u0627\u0632\u06cc \u0627\u0632 \u062c\u0641\u062a \u0646\u06cc\u0645\u0647 \u0644\u06af-\u06a9\u0627\u0646\u0648\u0646 (SLC) $ (v \u060c \u03b4) $ \u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 $ \u03b4 = ch $ \u060c $ c <1 $ \u0627\u0633\u062a \u060c \u06cc\u06a9 \u0645\u0639\u0642\u0648\u0644 \u0645\u0646\u0637\u0642\u06cc \u0627\u0633\u062a\u06cc\u06a9 \u0628\u062e\u0634 \u0639\u0645\u0648\u0645\u06cc\u067e\u0631\u067e\u0644\u0646 \u0627\u0632 $ H $.\u0628\u0631\u0627\u06cc \u0633\u0647 \u0628\u0631\u0627\u0628\u0631 \u060c \u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0646\u062a\u0627\u06cc\u062c \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc Iskovskikh-Mori-Mukai \u060c \u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0635\u0631\u06cc\u062d \u062f\u0631 \u0645\u0648\u0631\u062f \u0632\u06cc\u0631\u0645\u062c\u0645\u0648\u0639\u0647 \u0647\u0627\u06cc SNC \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u062f\u0647\u06cc\u0645.\u0628\u0647 \u0637\u0648\u0631 \u062e\u0627\u0635 \u060c \u0645\u0627 \u0648\u062c\u0648\u062f \u0627\u062a\u062d\u0627\u062f\u06cc\u0647 \u0647\u0627\u06cc v = $ y_1 \\ bigcup_d y_2 \\ subset \\ mathbb {p}^n $ \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 $ y_i $ \u0628\u0647 \u0635\u0648\u0631\u062a \u0636\u062f \u0636\u062f \u0627\u0646\u0639\u0637\u0627\u0641 \u067e\u0630\u06cc\u0631 (\u0628\u0647 \u0635\u0648\u0631\u062a \u062f\u0648\u0633\u0627\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u062f\u0648\u0633\u0627\u0646) \u062a\u0639\u0628\u06cc\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a \u060c \u0633\u0647 \u0628\u0631\u0627\u0628\u0631 \u0634\u062f\u0647 \u060c \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f $ $d $ \u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 $ d $ \u06cc\u0627 \u06cc\u06a9 \u0633\u0637\u062d del-pezzo \u06cc\u0627 \u06cc\u06a9 \u0633\u0637\u062d k3 $ $ (\u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u06cc\u06a9 \u0633\u0637\u062d \u0635\u0627\u0641 \u0628\u0627 \u0628\u0633\u062a\u0647 \u0646\u0631\u0645 \u0627\u0641\u0632\u0627\u0631\u06cc \u06a9\u0627\u0641\u06cc) \u0648 \u0635\u0627\u0641 \u06a9\u0631\u062f\u0646 \u0622\u0646\u0647\u0627 \u062f\u0631 $ \\ mathbb {p}^n $ \u0628\u0631\u0627\u06cc \u0635\u0627\u0641 \u06a9\u0631\u062f\u0646 fano \u06cc\u0627 calabi-\u0633\u0647 \u0628\u0631\u0627\u0628\u0631 YAU (\u0628\u0647 \u0633\u0647 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0628\u0633\u062a\u0647 \u0646\u0631\u0645 \u0627\u0641\u0632\u0627\u0631\u06cc \u0641\u0631\u0627\u0648\u0627\u0646) \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062e\u062a\u0644\u0641 $ N \u0628\u06cc\u0646 10 \u062f\u0644\u0627\u0631 \u0648 163 \u062f\u0644\u0627\u0631.\u062f\u0631 \u0645\u0648\u0627\u0631\u062f\u06cc \u06a9\u0647 \u0641\u06cc\u0628\u0631 \u0639\u0645\u0648\u0645\u06cc \u06cc\u06a9 \u0641\u0646\u0648\u062f \u0635\u0627\u0641 \u06cc\u0627 Calabi-yau \u0633\u0647 \u0628\u0631\u0627\u0628\u0631 \u0627\u0633\u062a \u060c \u0645\u06cc \u062a\u0648\u0627\u0646 $ c $ \u0631\u0627 \u0628\u0647 \u06af\u0648\u0646\u0647 \u0627\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f \u06a9\u0647 $ (v \u060c \u03b4) $ \u06cc\u06a9 \u062c\u0641\u062a calabi-yau \u0627\u0633\u062a \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u062f\u0631 \u0647\u0645\u0647 \u0645\u0648\u0627\u0631\u062f $ c $ \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0647 \u0637\u0648\u0631\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0634\u0648\u062f \u06a9\u0647 $ $(v \u060c \u03b4) $ \u06cc\u06a9 \u062c\u0641\u062a \u067e\u0627\u06cc\u062f\u0627\u0631 \u0627\u0633\u062a.\n\n\n[sc name=\"papertranslation\"][\/sc]\n<\/p>\n","protected":false},"excerpt":{"rendered":"

\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Projective smoothing of varieties with simple normal crossings \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0647\u0645\u0648\u0627\u0631\u0633\u0627\u0632\u06cc […]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"closed","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"product_cat":[15,21],"product_tag":[740,742],"class_list":{"0":"post-41028","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-15","7":"product_cat-21","8":"product_tag-algebraic-geometry","9":"product_tag-742","10":"pmpro-has-access","11":"desktop-align-left","12":"tablet-align-left","13":"mobile-align-left","15":"first","16":"instock","17":"downloadable","18":"shipping-taxable","19":"purchasable","20":"product-type-simple"},"yoast_head":"\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0647\u0645\u0648\u0627\u0631\u0633\u0627\u0632\u06cc \u067e\u0631\u0648\u062c\u06a9\u062a\u06cc\u0648 \u0627\u0646\u0648\u0627\u0639 \u0628\u0627 \u062a\u0642\u0627\u0637\u0639 \u0647\u0627\u06cc \u0645\u0639\u0645\u0648\u0644\u06cc \u0633\u0627\u062f\u0647 - 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