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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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, 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:	Date Event 2020 Published 6 January 2020 Accepted
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:	Publisher
Open Access Version:	ArXiv Publisher

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