English

Classification of Fano 4-folds with Lefschetz defect 3 and Picard number 5

Algebraic Geometry 2020-07-23 v1

Abstract

Let X be a smooth, complex Fano 4-fold, and rho(X) its Picard number. If X contains a prime divisor D with rho(X)-rho(D)>2, then either X is a product of del Pezzo surfaces, or rho(X)=5 or 6. In this setting, we completely classify the case where rho(X)=5; there are 6 families, among which one is new. We also deduce the classification of Fano 4-folds with rho(X)>4 with an elementary divisorial contraction sending a divisor to a curve.

Keywords

Cite

@article{arxiv.2007.11229,
  title  = {Classification of Fano 4-folds with Lefschetz defect 3 and Picard number 5},
  author = {Cinzia Casagrande and Eleonora A. Romano},
  journal= {arXiv preprint arXiv:2007.11229},
  year   = {2020}
}

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16 pages