Gianluca Pacienza

Nodal Curves with General Moduli on K3 Surfaces

We investigate the modular properties of nodal curves on a low genus K3 surface. We prove that a general genus g curve C is the normalization of a δ-nodal curve X sitting on a primitively polarized K3 surface S of degree 2p − 2, for 2 ≤ g = p − δ < p ≤ 11. The proof is based on a local deformation-theoretic analysis of the map from the stack of pairs (S, X) to the moduli stack of curves ℳ g that associates to X the isomorphism class [C] of its normalization.

Rational curves on general projective hypersurfaces

Let

SINGULAR CURVES ON A K3 SURFACE AND LINEAR SERIES ON THEIR NORMALIZATIONS

k

On the logarithmic Kobayashi conjecture

be an integer such that

Uniruledness of stable base loci of adjoint linear systems via Mori theory

1\leq k\leq n-5

Uniruledness of stable base loci of adjoint linear systems with and without Mori Theory

, and

ON THE UNIFORMITY OF THE IITAKA FIBRATION

X_{2n-2-k}\subset \mathbf P^n

On the nef cone of symmetric products of a generic curve

a general projective hypersurface of degree

Families of rational curves on holomorphic symplectic varieties and applications to 0-cycles

d=2n-2-k

On families of rational curves in the Hilbert square of a surface

. In this paper we prove that the only