Geodesic
Hodge Numbers and Deformations of Fano 3-Folds
Documenta mathematica, Tome 25 (2020), pp. 267-307.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14J30, 14C30, 14E30
Keywords: Fano 3-fold, Hodge numbers, deformation theory 
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     author = {Brown, Gavin and Fatighenti, Enrico},
     title = {Hodge {Numbers} and {Deformations} of {Fano} {3-Folds}},
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Brown, Gavin; Fatighenti, Enrico. Hodge Numbers and Deformations of Fano 3-Folds. Documenta mathematica, Tome 25 (2020), pp. 267-307. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a60/