On the Shafarevich and Tate conjectures for hyperkähler varieties.
Optimal bound for the number of -curves on extremal rational surfaces.
Persson's list of singular fibers for a rational elliptic surface.
Polytopes, quasi-minuscule representations and rational surfaces
We describe the relation between quasi-minuscule representations, polytopes and Weyl group orbits in Picard lattices of rational surfaces. As an application, to each quasi-minuscule representation we attach a class of rational surfaces, and realize such a representation as an associated vector bundle of a principal bundle over these surfaces. Moreover, any quasi-minuscule representation can be defined by rational curves, or their disjoint unions in a rational surface, satisfying certain natural...
Positivity results for Euler characteristics of singular surfaces.
Poznámka o Clebschově diagonální ploše
Poznámka o parabolické křivce plochy třetího stupně
Poznámky o ploše třetího stupně s oskulačním kuželem
Principe de Hasse et rang pour des courbes de genre 2 à jacobienne simple
Quelques plongements projectifs non speciaux de surfaces rationnelles.
Rank-3 stable bundles on rational rundle ruled surfaces.
Rational projectively Cohen-Macaulay surfaces of maximum degree.
In this paper we determine the greatest degree of a rational projectively Cohen-Macaulay (p.C.M.) surface V in PN and we study the surfaces which attain such maximum degree.
Rationality of Moduli spaces of torsion free sheaves over rational surfaces.
Rationally connected foliations on surfaces.
Real equivalence of complex matrix pencils and complex projections of real Segre varieties.
Real singular Del Pezzo surfaces and 3-folds fibred by rational curves, II
Let be a real smooth projective 3-fold fibred by rational curves such that is orientable. J. Kollár proved that a connected component of is essentially either Seifert fibred or a connected sum of lens spaces. Answering three questions of Kollár, we give sharp estimates on the number and the multiplicities of the Seifert fibres (resp. the number and the torsions of the lens spaces) when is a geometrically rational surface. When is Seifert fibred over a base orbifold , our result generalizes...
Recherches analytiques sur la surface du troisième ordre qui est la réciproque de la surface de Steiner
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...
Smooth curves on a cone which pass through its vertex.