On Fano 4-folds with Lefschetz defect 3

24-Feb-2021, 11:30-12:30 (3 years ago)

Abstract: We will talk about a classification result for some (smooth, complex) Fano 4-folds. We recall that if X is a Fano 4-fold, the Lefschetz defect delta(X) is an invariant of X defined as follows. Consider a prime divisor D in X and the restriction r: H^2(X,R)->H^2(D,R). Then delta(X) is the maximal dimension of ker(r), where D varies among all prime divisors in X. In a previous work, we showed that if X is not a product of surfaces, then delta(X) is at most 3, and if moreover delta(X)=3, then X has Picard number 5 or 6. We will explain that in the case where X has Picard number 5, there are 6 possible families for X, among which 4 are toric. This is a joint work with Eleonora Romano.

algebraic geometry

Audience: researchers in the topic

( video )


Fano Varieties and Birational Geometry

Organizers: Livia Campo, Alexander Kasprzyk*
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