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Hodge numbers and deformations of Fano 3-folds

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Brown, Gavin and Fatighenti, Enrico (2020) Hodge numbers and deformations of Fano 3-folds. Documenta Mathematica, 25 . pp. 267-307. doi:10.25537/dm.2020v25.267-307

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Official URL: http://dx.doi.org/10.25537/dm.2020v25.267-307

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Abstract

We show that index 1 Fano 3-folds which lie in weighted Grassmannians in their total anticanonical embedding have finite automorphism group, and we relate the deformation theory of any Fano 3-fold that has a K3 elephant to its Hodge theory. Combining these results with standard Gorenstein projection techniques calculates both the number of deformations and the Hodge numbers of most quasi-smooth Fano 3-folds in low codimension. This provides detailed new information for hundreds of families of Fano 3-folds.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Threefolds (Algebraic geometry) , Hodge theory, Deformations of singularities
Journal or Publication Title: Documenta Mathematica
Publisher: Deutsche Mathematiker Vereinigung
ISSN: 1431-0643
Official Date: 2020
Dates:
DateEvent
2020Published
6 January 2020Accepted
Date of first compliant deposit: 6 January 2020
Volume: 25
Page Range: pp. 267-307
DOI: 10.25537/dm.2020v25.267-307
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
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