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Classification of Fano fourfolds with large anticanonical base locus
Andreas Höring, Saverio Andrea Secci
We give a classification of smooth Fano fourfolds such that the base scheme of the anticanonical system is a smooth surface. As a consequence we show that there are exactly 22 defo…
K-polystability of Fano 4-folds with large Lefschetz defect
Eleonora A. Romano, Saverio A. Secci
In this paper, we investigate K-polystability on smooth complex Fano 4-folds with Lefschetz defect at least 2, focusing on the case of Lefschetz defect 3 and on Casagrande-Druel Fa…
Classifying Fano 4-folds with a rational fibration onto a 3-fold
Cinzia Casagrande, Saverio Andrea Secci
We study smooth, complex Fano 4-folds X with a rational contraction onto a 3-fold, namely a rational map X-->Y that factors as a sequence of flips X-->X' followed by a surjective m…
Fano fourfolds with large anticanonical base locus
Andreas Höring, Saverio Andrea Secci
A famous theorem of Shokurov states that a general anticanonical divisor of a smooth Fano threefold is a smooth K3 surface. This is quite surprising since there are several example…
Fano manifolds with Lefschetz defect 3
C. Casagrande, E. A. Romano, S. A. Secci
Let X be a smooth, complex Fano variety, and delta(X) its Lefschetz defect. It is known that if delta(X) is at least 4, then X is isomorphic to a product SxT, where dim T=dim X-2.…
Fano 4-folds having a prime divisor of Picard number 1
Saverio Andrea Secci
We give a complete classification of smooth, complex projective Fano 4-folds of Picard number 3 having a prime divisor of Picard number 1. They form 28 distinct families, and we co…
On the existence of Ulrich bundles on blown-up varieties at a point
Saverio Andrea Secci
The objective is to show the construction of an Ulrich vector bundle on the blowing-up of a nonsingular projective variety at a closed point, where the original…