Quadrics through a set of points and their syzygies.
Quelques plongements projectifs non speciaux de surfaces rationnelles.
Quelques résultats de Corrado Segre sur les surfaces réglées.
Relations in the canonical algebras on surfaces
Relative vanishing theorems I: applications to ample divisors.
Remarks on numerically positive line bundles on normal surfaces.
Remarks on the Nagata Conjecture
2000 Mathematics Subject Classification: 14C20, 14E25, 14J26.The famous Nagata Conjecture predicts the lowest degree of a plane curve passing with prescribed multiplicities through given points in general position. We explain how this conjecture extends naturally via multiple point Seshadri constants to ample line bundles on arbitrary surfaces. We show that if there exist curves of unpredictable low degree, then they must have equal multiplicities in all but possibly one of the given points. We...
Remarks on the postulation of zero-dimensional subschemes of projective space.
Representation stability for syzygies of line bundles on Segre–Veronese varieties
The rational homology groups of packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces (Segre–Veronese varieties). These complexes are a common generalization of the multidimensional chessboard complexes and of the matching complexes of complete uniform hypergraphs, whose study has been a topic of interest in combinatorial topology. We prove that the multivariate version of representation stability,...
Secant spaces and Clifford's theorem
Semipolarized nonruled surfaces with sectional genus two.
Seshadri constants and interpolation on commutative algebraic groups
In this article we study interpolation estimates on a special class of compactifications of commutative algebraic groups constructed by Serre. We obtain a large quantitative improvement over previous results due to Masser and the first author and our main result has the same level of accuracy as the best known multiplicity estimates. The improvements come both from using special properties of the compactifications which we consider and from a different approach based upon Seshadri constants and...
Slopes of effective divisors on the moduli space of stable curves.
Some remarks on the Severi varieties of surfaces in .
Some remarks on the study of good contractions.
Sous-variétés spéciales des variétés de Prym
Special divisors on curves on a K3 surface.
Special effect varieties in higher dimension.
Here we introduce the concept of special effect varieties in higher dimension and we generalize to Pn, n ≥ 3, the two conjectures given in [2] for the planar case. Finally, we propose some examples on the product of projective spaces and we show how these results fit with the ones of Catalisano, Geramita and Gimigliano.
Special line bundles on curves with involution.
Stable Curves and Special Divisors: Petri's Conjecture.