Gian Pietro Pirola

On the topological index of irregular surfaces

We study the topological index of some irregular surfaces that we call generalized Lagrangian. We show that under certain hypotheses on the base locus of the Lagrangian system the topological index is non-negative. For the minimal surfaces of general type with q = 4 and pg = 5 we prove the same statement without any hypothesis.

Symmetries, quotients and Kähler-Einstein metrics

Abstract We consider Fano manifolds M that admit a collection of finite automorphism groups G 1, …, Gk , such that the quotients M/Gi are smooth Fano manifolds possessing a Kähler-Einstein metric. Under some numerical and smoothness assumptions on the ramification divisors, we prove that M admits a Kähler-Einstein metric too.

Monodromy of projective curves

The uniform position principle states that, given an irreducible nondegenerate curve C in the projective r-space

Density of elliptic solitons

P^r

Chern character of degeneracy loci and curves of special divisors

, a general (r-2)-plane L is uniform, that is, projection from L induces a rational map from C to

Brill–Noether loci for divisors on irregular varieties

P^1

Continuous families of divisors, paracanonical systems and a new inequality for varieties of maximal Albanese dimension

whose monodromy group is the full symmetric group. In this paper we show the locus of non-uniform (r-2)-planes has codimension at least two in the Grassmannian for a curve C with arbitrary singularities. This result is optimal in

On rational maps from a general surface in to surfaces of general type

P^2

Algebraic functions with even monodromy

. For a smooth curve C in

Generic Torelli theorem for Prym varieties of ramified coverings

P^3