Hodge numbers and deformations of Fano 3-folds

  title={Hodge numbers and deformations of Fano 3-folds},
  author={Gavin Brown and E. Fatighenti},
  journal={arXiv: Algebraic Geometry},
  • Gavin Brown, E. Fatighenti
  • Published 2020
  • Mathematics
  • arXiv: Algebraic Geometry
  • 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 quasismooth Fano 3-folds in low codimension. This provides detailed new information for hundreds of families of… CONTINUE READING
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