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Authors: Felten, Simon
Filip, Matej
Ruddat, Helge
Title: Smoothing toroidal crossing spaces
Online publication date: 16-Nov-2021
Language: english
Abstract: We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces. The main approach is to study log structures that are incoherent on a subspace of codimension 2 and prove a Hodge–de Rham degeneration theorem for such log spaces that also settles a conjecture by Danilov. We show that the homotopy equivalence between Maurer–Cartan solutions and deformations combined with Batalin–Vilkovisky theory can be used to obtain smoothings. The construction of new Calabi–Yau and Fano manifolds as well as Frobenius manifold structures on moduli spaces provides potential applications.
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: Forum of mathematics : Pi
Pages or article number: e7
Publisher: Cambridge Univ. Press
Publisher place: Cambridge
Issue date: 2021
ISSN: 2050-5086
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Appears in collections:JGU-Publikationen

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