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.
On the non-defectivity of non weak-defectivity of Segre-Veronese embeddings of products of projective spaces.
On the number of connected components of real abelian varieties that admit sufficiently many compley multiplications.
On the number of singular ponts of a real projective hypersurface.
On the osculatory behaviour of higher dimensional projective varieties.
We explore the geometry of the osculating spaces to projective verieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the existence of inflectionary points.
On the projective normality of complete linear series on an algebraic curve.
On the projective normality of the adjunction bundles.
On the projectivity of the moduli spaces of curves.
On the quantum cohomology of the plane, old and new, and a K3 analogue.
On the real X -ranks of points of P n (R) with respect to a real variety X ⊂ P n
Let X ⊂ Pn be an integral and non-degenerate m-dimensional variety defined over R. For any P ∈ Pn(R) the real X-rank r x,R(P) is the minimal cardinality of S ⊂ X(R) such that P ∈ . Here we extend to the real case an upper bound for the X-rank due to Landsberg and Teitler.
On the secant varieties to the osculating variety of a Veronese surface
In this paper we study the k-th osculating variety of the order d Veronese embedding of P n. In particular, for k=n=2 we show that the corresponding secant varieties have the expected dimension except in one case.
On the second sectional geometric genus of quasi-polarized manifolds.