O. Debarre

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math.AG2002

Sur une conjecture de Mukai

L. Bonavero, C. Casagrande, O. Debarre +1

Generalizing a question of Mukai, we conjecture that a Fano manifold $X$ with Picard number $ρ_{X}$ and pseudo-index $ι_{X}$ satisfies $ρ_{X} (ι_{X} - 1) \leq dim (X)$ . We prove this inequali…

math.AG1998

Lieux de dégénérescence (Degeneracy loci)

O. Debarre

We prove Lefschetz type theorems for cohomology groups and Picard groups of degeneracy loci for vector bundle maps. We also treat the case of antisymmetric maps.