ملف:Barbara Fantechi on Algebraic Geometry at Stanford.jpg
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English: Barbara Fantechi (Oct. 16, 2020): Infinitesimal deformations of semi-smooth varieties
This is a report on joint work with Marco Franciosi and Rita Pardini. Generalizing the standard definition for surfaces, we call a variety X (over an algebraically closed field of characteristic not 2) {\em semi-smooth} if its singularities are \'etale locally either uv=0 or u^2=v^2w (pinch point); equivalently, if X can be obtained by gluing a smooth variety (the normalization of X) along an involution (with smooth quotient) on a smooth divisor. They are the simplest singularities for non normal, KSBA-stable surfaces. For a semi-smooth variety X, we calculate the tangent sheaf T_X and the infinitesimal deformations sheaf {\mathcal T}^1_X:={\mathcal E}xt^1(\Omega_X,\mathcal O_X) which determine the infinitesimal deformations and smoothability of X. As an application, we use Tziolas' formal smoothability criterion to show that every stable semi-smooth Godeaux surface (classified by Franciosi, Pardini and S\"onke) corresponds to a smooth point of the KSBA moduli space, in the closure of the open locus of smooth surfaces. |
⧼wm-license-information-date⧽ | 2021 |
⧼wm-license-information-source⧽ | Barbara Fantechi (Oct. 16, 2020): Infinitesimal deformations of semi-smooth varieties at 1:00:41, cropped, brightened |
⧼wm-license-information-author⧽ | Algebraic Geometry at Stanford |
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زمن/تاريخ | صورة مصغرة | الأبعاد | مستخدم | تعليق | |
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حالي | ★ مراجعة معتمدة 10:54، 10 أكتوبر 2023 | 602 × 789 (71 كيلوبايت) | Pastakhov (نقاش | مساهمات) | Upload https://upload.wikimedia.org/wikipedia/commons/2/24/Barbara_Fantechi_on_Algebraic_Geometry_at_Stanford.jpg |
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