Fano fivefolds of index two with blow-up structure
We classify Fano fivefolds of index two which are blow-ups of smooth manifolds along a smooth center.
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arXiv subjects
Gianluca Occhetta
Publications and source records attributed to Gianluca Occhetta.
Fano manifolds and blow-ups of low-dimensional subvarieties
We study Fano manifolds of pseudoindex greater than one and dimension greater than five, which are blow-ups of smooth varieties along smooth centers of dimension equal to the pseudoindex of the manifold. We obtain a classification of the possible cones of curves of these manifolds, and we prove that there is only one such manifold without a fiber type elementary contraction.
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The cone of curves of Fano varieties of coindex four
We classify the cones of curves of Fano varieties of dimension greater or equal than five and (pseudo)index dim X -3, describing the number and type of their extremal rays.
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Ruled Fano fivefolds of index two
We classify Fano fivefolds of index two which are projectivization of rank two vector bundles over four dimensional manifolds.
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Fano manifolds with long extremal rays
Let X be a Fano manifold of pseudoindex i_X whose Picard number is at least two and let R be an extremal ray of X with exceptional locus Exc(R). We prove an inequality which bounds the length of R in terms of i_X and of the dimension of Exc(R) and we investigate the border cases. In particular we classify Fano manifolds X of pseudoindex i_X obtained blowing up a smooth variety Y along a smooth subvariety T such that dim T < i_X.
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Generalized Mukai conjecture for special Fano varieties
Let X be a Fano variety of dimension n, pseudoindex i_X and Picard number ρ_X. A generalization of a conjecture of Mukai says that ρ_X(i_X-1)\le n. We prove that the conjecture holds if: a) X has pseudoindex i_X \ge \frac{n+3}{3} and either has a fiber type extremal contraction or does not have small extremal contractions b) X has dimension five.
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On Euler-Jaczewski sequence and Remmert-Van de Ven problem for toric varieties
Let X be a complete toric variety and let Y be a smooth projective variety with Picard number one. We prove that, if there exists a surjective morphism from X to Y, then Y is a projective space.
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Special rays in the Mori cone of a projective variety
Let $X$ be a smooth $n$-dimensional projective variety over an algebraically closed field $k$ such that $K_X$ is not nef. We give a characterization of non nef extremal rays of $X$ of maximal length (i.e of length $n-1$); in the case of $\ch(k) = 0$ we also characterize non nef rays of length $n-2$.
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Ample vector bundles with sections vanishing on special varieties
Let E be an ample vector bundle of rank r on a complex projective manifold X such that there exists a section $s \in Γ(\cal E)$ whose zero locus Z = (s = 0) is a smooth submanifold of the expected dimension dim X - r: = n -r. Assume that Z is not minimal; we investigate the hypothesis under which the extremal contractions of Z can be lifted to X. Finally we study in detail the cases in which Z is a scroll, a quadric bundle or a del Pezzo fibration.
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