Finiteness for self-dual classes in integral variations of Hodge structure

Benjamin Bakker; Thomas W. Grimm; Christian Schnell; Jacob Tsimerman

doi:10.48550/arXiv.2112.06995

Finiteness for self-dual classes in integral variations of Hodge structure

Benjamin Bakker
, Thomas W. Grimm
, Christian Schnell
, Jacob Tsimerman

Research output: Working paper › Preprint › Academic

Abstract

We generalize the finiteness theorem for the locus of Hodge classes with fixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodge classes to self-dual classes. The proof uses the definability of period mappings in the o-minimal structure $\mathbb{R}_{\mathrm{an},\exp}$.

Original language	English
Publisher	arXiv
Pages	1-27
DOIs	https://doi.org/10.48550/arXiv.2112.06995
Publication status	Published - 13 Dec 2021

Bibliographical note

27 pages. Comments are welcome at any time!

Keywords

math.AG
hep-th

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10.48550/arXiv.2112.06995

2112.06995v1Submitted manuscript, 347 KBLicence: CC BY

https://arxiv.org/abs/2112.06995Licence: CC BY

Cite this

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title = "Finiteness for self-dual classes in integral variations of Hodge structure",

abstract = "We generalize the finiteness theorem for the locus of Hodge classes with fixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodge classes to self-dual classes. The proof uses the definability of period mappings in the o-minimal structure \$\textbackslash{}mathbb\{R\}\_\{\textbackslash{}mathrm\{an\},\textbackslash{}exp\}\$. ",

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author = "Benjamin Bakker and Grimm, \{Thomas W.\} and Christian Schnell and Jacob Tsimerman",

note = "27 pages. Comments are welcome at any time!",

year = "2021",

month = dec,

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doi = "10.48550/arXiv.2112.06995",

language = "English",

pages = "1--27",

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AU - Grimm, Thomas W.

AU - Schnell, Christian

AU - Tsimerman, Jacob

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PY - 2021/12/13

Y1 - 2021/12/13

N2 - We generalize the finiteness theorem for the locus of Hodge classes with fixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodge classes to self-dual classes. The proof uses the definability of period mappings in the o-minimal structure $\mathbb{R}_{\mathrm{an},\exp}$.

AB - We generalize the finiteness theorem for the locus of Hodge classes with fixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodge classes to self-dual classes. The proof uses the definability of period mappings in the o-minimal structure $\mathbb{R}_{\mathrm{an},\exp}$.

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KW - hep-th

U2 - 10.48550/arXiv.2112.06995

DO - 10.48550/arXiv.2112.06995

M3 - Preprint

SP - 1

EP - 27

BT - Finiteness for self-dual classes in integral variations of Hodge structure

PB - arXiv

ER -

Finiteness for self-dual classes in integral variations of Hodge structure

Abstract

Bibliographical note

Keywords

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Cite this