On the finiteness of rational curves on quintic threefolds
On the generation of certain bundles over P3.
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 quadrics and their degenerations.
On the gonality of curves in
Here we study the gonality of several projective curves which arise in a natural way (e.gċurves with maximal genus in , curves with given degree and genus for all possible , if and with large for arbitrary ).
On the graded Betti numbers for large finite subsets of curves
We prove a recent conjecture of S. Lvovski concerning the periodicity behaviour of top Betti numbers of general finite subsets with large cardinality of an irreducible curve C ⊂ ℙⁿ.
On the group orders of elliptic curves over finite fields
On the Hilbert function of curvilinear zero-dimensional subschemes of projective spaces
Here we show the existence of strong restrictions for the Hilbert function of zerodimensional curvilinear subschemes of P n with one point as support and with high regularity index.
On the Hilbert Scheme of Curves of Maximal Genus in a Projective Space.
On the Hilbert scheme of Palatini threefolds.
On the homogeneous ideal of collinear punctual subschemes of P2.
On the homogeneous ideal of the generic union of lines in ...3.ö
On the homogeneous ideal of unreduced projective schemes.
On the homology of the Hubert scheme of points in the plane.
On the hypersurfaces containing a general projective curve
On the inseparable degrees of the Gauss map and the projection of the conormal variety to the dual fo higher order for space curves.
On the intersection multiplicity of improper components in algebraic geometry
On the k-regularity of some proyective manifolds.
The conjecture on the (degree-codimension + 1) - regularity of projective varieties is proved for smooth linearly normal polarized varieties (X,L) with L very ample, for low values of Delta(X,L) = degree-codimension-1. Results concerning the projective normality of some classes of special varieties including scrolls over curves of genus 2 and quadric fibrations over elliptic curves, are proved.
On the local differential geometry of complete intersections
On the moduli b-divisors of lc-trivial fibrations
Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite cover. As an application, we obtain that the moduli part of an lc-trivial fibration is b-nef and abundant by Ambro’s result on klt-trivial fibrations.