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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 ISSN 1431-0643.
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Official URL: http://dx.doi.org/10.25537/dm.2020v25.267-307
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 | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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 (Creative Commons) | ||||||
Date of first compliant deposit: | 6 January 2020 | ||||||
Date of first compliant Open Access: | 10 January 2020 | ||||||
Related URLs: | |||||||
Open Access Version: |
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