Geodesic
Hodge Numbers and Deformations of Fano 3-Folds
Documenta mathematica, Tome 25 (2020), pp. 267-307
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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.
DOI : 10.4171/dm/747
Classification : 14C30, 14E30, 14J30
Mots-clés : deformation theory, Hodge numbers, Fano 3-fold 
@article{10_4171_dm_747,
     author = {Gavin Brown and Enrico Fatighenti},
     title = {Hodge {Numbers} and {Deformations} of {Fano} {3-Folds}},
     journal = {Documenta mathematica},
     pages = {267--307},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/747},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/747/}
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Gavin Brown; Enrico Fatighenti. Hodge Numbers and Deformations of Fano 3-Folds. Documenta mathematica, Tome 25 (2020), pp. 267-307. doi: 10.4171/dm/747

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