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Density of rational points on cyclic covers of n

Ritabrata Munshi (2009)

Journal de Théorie des Nombres de Bordeaux

We obtain upper bound for the density of rational points on the cyclic covers of n . As n our estimate tends to the conjectural bound of Serre.

Derived category of toric varieties with small Picard number

Laura Costa, Rosa Miró-Roig (2012)

Open Mathematics

This paper aims to construct a full strongly exceptional collection of line bundles in the derived category D b(X), where X is the blow up of ℙn−r ×ℙr along a multilinear subspace ℙn−r−1×ℙr−1 of codimension 2 of ℙn−r ×ℙr. As a main tool we use the splitting of the Frobenius direct image of line bundles on toric varieties.

Derived invariance of the number of holomorphic 1 -forms and vector fields

Mihnea Popa, Christian Schnell (2011)

Annales scientifiques de l'École Normale Supérieure

We prove that smooth projective varieties with equivalent derived categories have isogenous Picard varieties. In particular their irregularity and number of independent vector fields are the same. This implies that all Hodge numbers are the same for arbitrary derived equivalent threefolds, as well as other consequences of derived equivalence based on numerical criteria.

Derived quot schemes

Ionuţ Ciocan-Fontanine, Mikhail Kapranov (2001)

Annales scientifiques de l'École Normale Supérieure

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