The dualizing sheaf on first-order deformations of toric surface singularities
-
Klaus Altmann
and
János Kollár
Abstract
We explicitly describe infinitesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Kollár–Shepherd-Barron (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.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: CRC 647
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1362960
Funding statement: Partial financial support to Klaus Altmann was provided by the DFG via the CRC 647 and to János Kollár by the NSF under grant number DMS-1362960.
Acknowledgements
We would like to thank F.-O. Schreyer for many fruitful discussions and initiating the contact on this topic. Thanks to Jan Stevens for finding mistakes in the originally submitted arXiv version and to the anonymous referee for valuable suggestions.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Homotopy techniques for tensor decomposition and perfect identifiability
- Schottky groups acting on homogeneous rational manifolds
- Limit linear series for curves not of compact type
- Uniform congruence counting for Schottky semigroups in SL2(𝐙)
- The dualizing sheaf on first-order deformations of toric surface singularities
- Embedded minimal surfaces of finite topology
- Spectral gap characterization of full type III factors
- On the universal cover and the fundamental group of an RCD*(K,N)-space
- Calabi–Yau and fractional Calabi–Yau categories
Articles in the same Issue
- Frontmatter
- Homotopy techniques for tensor decomposition and perfect identifiability
- Schottky groups acting on homogeneous rational manifolds
- Limit linear series for curves not of compact type
- Uniform congruence counting for Schottky semigroups in SL2(𝐙)
- The dualizing sheaf on first-order deformations of toric surface singularities
- Embedded minimal surfaces of finite topology
- Spectral gap characterization of full type III factors
- On the universal cover and the fundamental group of an RCD*(K,N)-space
- Calabi–Yau and fractional Calabi–Yau categories
