The dualizing sheaf on first-order deformations of toric surface singularities

Klaus Altmann; János Kollár

doi:10.1515/crelle-2016-0063

The dualizing sheaf on first-order deformations of toric surface singularities

Klaus Altmann, János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We explicitly describe infinitesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Kollár-ShepherdBarron (KSB) and Viehweg. The conclusion is that in many cases these three notions are different from each other. In particular, we see that while the KSB and the Viehweg versions of the moduli space of surfaces of general type have the same underlying reduced subscheme, their infinitesimal structures are different.

Original language	English (US)
Pages (from-to)	137-158
Number of pages	22
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2019
Issue number	753
DOIs	https://doi.org/10.1515/crelle-2016-0063
State	Published - Aug 1 2019

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1515/crelle-2016-0063

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abstract = "We explicitly describe infinitesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Koll{\'a}r-ShepherdBarron (KSB) and Viehweg. The conclusion is that in many cases these three notions are different from each other. In particular, we see that while the KSB and the Viehweg versions of the moduli space of surfaces of general type have the same underlying reduced subscheme, their infinitesimal structures are different.",

author = "Klaus Altmann and J{\'a}nos Koll{\'a}r",

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AU - Kollár, János

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N2 - We explicitly describe infinitesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Kollár-ShepherdBarron (KSB) and Viehweg. The conclusion is that in many cases these three notions are different from each other. In particular, we see that while the KSB and the Viehweg versions of the moduli space of surfaces of general type have the same underlying reduced subscheme, their infinitesimal structures are different.

AB - We explicitly describe infinitesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Kollár-ShepherdBarron (KSB) and Viehweg. The conclusion is that in many cases these three notions are different from each other. In particular, we see that while the KSB and the Viehweg versions of the moduli space of surfaces of general type have the same underlying reduced subscheme, their infinitesimal structures are different.

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JF - Journal fur die Reine und Angewandte Mathematik

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ER -

The dualizing sheaf on first-order deformations of toric surface singularities

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