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A classification theorem on Fano bundles

Roberto Muñoz, Luis E. Solá Conde, Gianluca Occhetta (2014)

Annales de l’institut Fourier

In this paper we classify rank two Fano bundles on Fano manifolds satisfying H 2 ( X , ) H 4 ( X , ) . The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization ( ) , that allows us to obtain the cohomological invariants of X and . As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.

Birational positivity in dimension 4

Behrouz Taji (2014)

Annales de l’institut Fourier

In this paper we prove that for a nonsingular projective variety of dimension at most 4 and with non-negative Kodaira dimension, the Kodaira dimension of coherent subsheaves of Ω p is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an X provided that X has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.

Bridgeland-stable moduli spaces for K -trivial surfaces

Daniele Arcara, Aaron Bertram (2013)

Journal of the European Mathematical Society

We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface S and describe “wall-crossing behavior” for objects with the same invariants as 𝒪 C ( H ) when H generates Pic ( S ) and C H . If, in addition, S is a K 3 or Abelian surface, we use this description to construct a sequence of fine moduli spaces of Bridgeland-stable objects via Mukai flops and generalized elementary modifications of the universal coherent sheaf. We also discover a natural...

Classes de cohomologie positives dans les variétés kählériennes compactes

Olivier Debarre (2004/2005)

Séminaire Bourbaki

Étant donnée une variété kählérienne compacte X , on étudie dans l’espace vectoriel réel de cohomologie de Dolbeault H 1 , 1 ( X , 𝐑 ) H 2 ( X , 𝐑 ) le cône convexe des classes de Kähler ainsi que celui, plus grand, des classes de courants positifs fermés de type ( 1 , 1 ) . Lorsque X est projective, les traces de ces cônes sur l’espace de Néron–Severi NS ( X ) 𝐑 H 1 , 1 ( X , 𝐑 ) engendré par les classes entières sont respectivement le cône des classes de diviseurs amples et l’adhérence de celui des classes de diviseurs effectifs.

Compact Kähler manifolds with compactifiable universal cover

Benoît Claudon, Andreas Höring (2013)

Bulletin de la Société Mathématique de France

In this appendix, we observe that Iitaka’s conjecture fits in the more general context of special manifolds, in which the relevant statements follow from the particular cases of projective and simple manifolds.

Contractions of smooth varieties. II. Computations and applications

Marco Andreatta, Jarosław A. Wiśniewski (1998)

Bollettino dell'Unione Matematica Italiana

Una contrazione su una varietà proiettiva liscia X è data da una mappa φ : X Z propria, suriettiva e a fibre connesse in una varietà irriducibile normale Z . La contrazione si dice di Fano-Mori se inoltre - K X è φ -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...

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