Interessi scientifici

(1) Linear systems and vector bundles on curves: Brill–Noether theory of line bundles and of rank-two semistable vector bundles of given degree/determinant, moduli spaces, (uni)rationality questions, Hilbert schemes of curves and surface scrolls in projective spaces

(2) Ulrich bundles on smooth projective varieties: moduli spaces and Ulrich trichotomy of projective varieties (Ulrich-finite, tame or wild);

(3) Classification of algebraic varieties and their families: Fano threefolds and Torelli-type theorems, ruled varieties over curves/surfaces and the study of their Hilbert schemes;

(4) Curves and their moduli: families of singular curves on smooth projective varieties: existence and gaps of geometric genera and connections with hyperbolocity of log pairs, number of moduli families of curves, Brill-Noether theory for the family, extended Gaussian maps, degeneration techniques and applications;

(5) Algebraic surfaces: classification of surfaces of general type and of their moduli spaces via degenerations (obstructing/unobstructing the smoothability of combinatorial configurations of planes); geometry of the moduli spaces of polarized K3 surfaces (partial compactifications, d-semistability as Friedman, Persson–Pinkham, etc.);

(6) Covering families of curves covering and connecting gonality of very general hypersurfaces of given degree, their relation with irrationality invariants of the hypersurfaces;

(7) Subloci in the moduli space M_g: subloci defined by geometric conditions on families of curves;

(8) Hyperkähler varieties: geometric description of r-dimensional rational varieties in the Hilbert scheme Hilb^d(S), where S is a K3 surface, in terms of families of singular curves on S whose normalizations admit unexpected linear series of degree d and dimension r; applications to the Mori theory of Hilb^d(S); unexpected involutions on Hilb^2(S) for a K3 surface S with cyclic Picard group via Mukai's description of S as a suitable Brill–Noether locus.