Hodge Numbers and Deformations of Fano 3-Folds

  • Gavin Brown

    Mathematics Institute, University of Warwick, Coventry CV4 7A, United Kingdom
  • Enrico Fatighenti

    Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
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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.

Cite this article

Gavin Brown, Enrico Fatighenti, Hodge Numbers and Deformations of Fano 3-Folds. Doc. Math. 25 (2020), pp. 267–307

DOI 10.4171/DM/747