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Authors: Felten, Simon
Title: Log smooth deformation theory via Gerstenhaber algebras
Online publication date: 12-Jan-2022
Language: english
Abstract: We construct a k[[Q]]-linear predifferential graded Lie algebra L∙X0/S0 associated to a log smooth and saturated morphism f0:X0→S0 and prove that it controls the log smooth deformation functor. This provides a geometric interpretation of a construction in Chan et al. (Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties, 2019. arXiv:1902.11174) whereof L∙X0/S0 is a purely algebraic version. Our proof crucially relies on studying deformations of the Gerstenhaber algebra of polyvector fields; this method is closely related to recent developments in mirror symmetry.
DDC: 510 Mathematik
510 Mathematics
Institution: Johannes Gutenberg-Universität Mainz
Department: FB 08 Physik, Mathematik u. Informatik
Place: Mainz
Version: Published version
Publication type: Zeitschriftenaufsatz
License: CC-BY
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Journal: Manuscripta mathematica
Pages or article number: 1
Publisher: Springer
Publisher place: Berlin u.a.
Issue date: 2022
ISSN: 1432-1785
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Appears in collections:JGU-Publikationen

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