Journal article
Smoothing toroidal crossing spaces
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Version of record, pdf, 750.8KB, Terms of use)
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- Publisher copy:
- 10.1017/fmp.2021.8
Authors
- Publisher:
- Cambridge University Press
- Journal:
- Forum of Mathematics, Pi More from this journal
- Volume:
- 9
- Article number:
- e7
- Publication date:
- 2021-08-19
- Acceptance date:
- 2021-07-18
- DOI:
- EISSN:
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2050-5086
- Language:
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English
- Pubs id:
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2031782
- Local pid:
-
pubs:2031782
- Deposit date:
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2024-09-23
Terms of use
- Copyright holder:
- Felten et al
- Copyright date:
- 2021
- Rights statement:
- © The Author(s), 2021. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Licence:
- CC Attribution (CC BY)
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