On the Cynk-Hulek criterion for crepant resolutions of double covers
| Autor: | Adam Logan, Colin Ingalls |
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| Rok vydání: | 2022 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Double cover Divisor 010102 general mathematics Field (mathematics) 01 natural sciences Primary decomposition Mathematics::Algebraic Geometry Intersection 0103 physical sciences Crepant resolution Tangent space 010307 mathematical physics 0101 mathematics Variety (universal algebra) Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra. 226:106901 |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2021.106901 |
| Popis: | A collection A = { D 1 , … , D n } of divisors on a smooth variety X is an arrangement if the intersection of every subset of A is smooth. We show that, if X is defined over a field of characteristic not equal to 2, a double cover of X ramified on an arrangement has a crepant resolution under additional hypotheses. Namely, we assume that all intersection components that change the canonical divisor when blown up are splayed , a property of the tangent spaces of the components first studied by Faber. This strengthens a result of Cynk and Hulek, which requires a stronger hypothesis on the intersection components. Further, we study the singular subscheme of the union of the divisors in A and prove that it has a primary decomposition where the primary components are supported on exactly the subvarieties which are blown up in the course of constructing the crepant resolution of the double cover. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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