We use wall-crossing with respect to Bridgeland stability conditions to systematically study
the birational geometry of a moduli space MM of stable sheaves on a K3 surface XX:(a) We …

Let ξ be the Chern character of a stable coherent sheaf on P2. We compute the cone of
effective divisors on the moduli space M (ξ) of semistable sheaves on P2 with Chern …

Manin's conjecture predicts the rate of growth of rational points of a bounded height after
removing those lying on an exceptional set. We study whether the exceptional set in Manin's …

General hyperplane sections of a Fano threefold Y of index 2 and Picard rank 1 are del
Pezzo surfaces, and their Picard group is related to a root system. To the corresponding …

Fix a Chern character of a stable sheaf on the plane. Assume either the rank is at most 6 or
the rank and first Chern class are coprime and the discriminant is sufficiently large. We use …

MORI CONES OF HOLOMORPHIC SYMPLECTIC VARIETIES OF K3 TYPE Introduction Let X
be an irreducible holomorphic symplectic manifold. Page 1 MORI CONES OF HOLOMORPHIC …

We prove that the kth Gaussian map γ H k γ^k_H is surjective on a polarized unnodal
Enriques surface (S, H) (S,H) with φ (H)> 2 k+ 4 φ(H)>2k+4. In particular, as a consequence …

The birational geometry of moduli spaces of sheaves on the projective plane | SpringerLink
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We determine the automorphism group of the Hilbert scheme of two points on a generic
projective K3 surface of any polarization. We obtain in particular new examples of Hilbert …

Over the last few years, wall-crossing for Bridgeland stability conditions has led to a large
number of results in algebraic geometry, particular on birational geometry of moduli spaces …