On contractions of extremal rays of Fano manifolds.
Length of Extremal Rays and Generalized Adjunction.
Fano manifolds and quadric bundles.
On Fano Manifolds of large index.
On a conjecture of Mukai.
On Bănică sheaves and Fano manifolds
Fano bundles of rank 2 on surfaces
Contractions of smooth varieties. II. Computations and applications
Una contrazione su una varietà proiettiva liscia è data da una mappa propria, suriettiva e a fibre connesse in una varietà irriducibile normale . La contrazione si dice di Fano-Mori se inoltre è -ampio. Nel lavoro, naturale seguito e completamento delle ricerche introdotte in [A-W3], si studiano diversi aspetti delle contrazioni di Fano-Mori attraverso esempi (capitolo 1) e teoremi di struttura (capitoli 3 e 4). Si discutono anche alcune applicazioni allo studio di morfismi birazionali propri...
On quasihomogeneous manifolds – via Brion-Luna-Vust theorem
We consider a smooth projective variety on which a simple algebraic group acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of with the induced action of on the normal bundle of a closed orbit of the action. We get effective results in case and .
On geometry of binary symmetric models of phylogenetic trees
We investigate projective varieties which are binary symmetric models of trivalent phylogenetic trees. We prove that they have Gorenstein terminal singularities and are Fano varieties of index 4 and dimension equal to the number of edges of the tree in question. Moreover any two such varieties which are of the same dimension are deformation equivalent, that is, they are in the same connected component of the Hilbert scheme of the projective space. As an application we provide a simple formula for...
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