Local topological obstruction for divisors
| Autor: | Indranil Biswas, Ananyo Dan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Divisor
General Mathematics Infinitesimal semi-regularity map Topology 01 natural sciences Lift (mathematics) Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry FOS: Mathematics Hodge locus 0101 mathematics Algebraic Geometry (math.AG) Projective variety Mathematics Fundamental class deformation of linear systems Noether-Lefschetz locus 010102 general mathematics Obstruction theories 14B10 14B15 14C30 14C20 14C25 14D07 Cohomology 010101 applied mathematics Obstruction theory Locus (mathematics) |
| Zdroj: | BIRD: BCAM's Institutional Repository Data instname |
| Popis: | Given a smooth, projective variety $X$ and an effective divisor $D\,\subseteq\, X$, it is well-known that the (topological) obstruction to the deformation of the fundamental class of $D$ as a Hodge class, lies in $H^2(\mathcal{O}_X)$. In this article, we replace $H^2(\mathcal{O}_X)$ by $H^2_D(\mathcal{O}_X)$ and give an analogous topological obstruction theory. We compare the resulting local topological obstruction theory with the geometric obstruction theory (i.e., the obstruction to the deformation of $D$ as an effective Cartier divisor of a first order infinitesimal deformations of $X$). We apply this to study the jumping locus of families of linear systems and the Noether-Lefschetz locus. Finally, we give examples of first order deformations $X_t$ of $X$ for which the cohomology class $[D]$ deforms as a Hodge class but $D$ does not lift as an effective Cartier divisor of $X_t$. To appear in Revista Matem\'atica Complutense |
| Databáze: | OpenAIRE |
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