On the Existence of Analytic Contractions.
On the genus of reducible surfaces and degenerations of surfaces
We deal with a reducible projective surface with so-called Zappatic singularities, which are a generalization of normal crossings. First we compute the -genus of , i.e. the dimension of the vector space of global sections of the dualizing sheaf . Then we prove that, when is smoothable, i.e. when is the central fibre of a flat family parametrized by a disc, with smooth general fibre, then the -genus of the fibres of is constant.
On the geometry of moduli of curves and line bundles
Here we focus on the geometry of , the compactification of the universal Picard variety constructed by L. Caporaso. In particular, we show that the moduli space of spin curves constructed by M. Cornalba naturally injects into and we give generators and relations of the rational Picard group of , extending previous work by A. Kouvidakis.
On the geometry of quadrics and their degenerations.
On the Graded Ring of Hubert Modular Forms Associated with Q (|..5).
On the graph labellings arising from phylogenetics
We study semigroups of labellings associated to a graph. These generalise the Jukes-Cantor model and phylogenetic toric varieties defined in [Buczynska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460]. Our main theorem bounds the degree of the generators of the semigroup by g + 1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.
On the Hilbert Scheme of Curves in Higher-dimensional Projective Space.
On the Hodge spectral sequence for some classes of non-complete algebraic manifolds.
On the homotopy of the complement to plane algebraic curves.
On the Infinitesimal Torelli Theorem for Certain irregular Surfaces of General Type.
On the Invariants of Base Changes of Pencils of Curves, I.
On the Kodaira Dimension of the Moduli Space of Curves.
On the Kodaira dimension of the moduli space of curves, II. The even-genus case.
On the Milnor fibrations of weighted homogeneous polynomials
On the minimal number of singular fibres in a family of surfaces of general type.
On the mini-superambitwistor space and super-Yang-Mills theory.
On the moduli of reflexive sheaves on a surface with rational double points.
On the moduli of stable vector bundles on a Hirzebruch surface.
On the Monodromy Group of Plane Curve Singularities.
On the motives of moduli of chains and Higgs bundles
We take another approach to Hitchin’s strategy of computing the cohomology of moduli spaces of Higgs bundles by localization with respect to the circle action. Our computation is done in the dimensional completion of the Grothendieck ring of varieties and starts by describing the classes of moduli stacks of chains rather than their coarse moduli spaces. As an application we show that the -torsion of the Jacobian acts trivially on the middle dimensional cohomology of the moduli space of twisted...