On a birational classification of bundles and reflexive sheaves on surfaces
On a geometric property of the normal bundle of surfaces in IP4.
On a spanned tautological bundle.
On coverings of simple abelian varieties
To any finite covering of degree between smooth complex projective manifolds, one associates a vector bundle of rank on whose total space contains . It is known that is ample when is a projective space ([Lazarsfeld 1980]), a Grassmannian ([Manivel 1997]), or a Lagrangian Grassmannian ([Kim Maniel 1999]). We show an analogous result when is a simple abelian variety and does not factor through any nontrivial isogeny . This result is obtained by showing that is -regular in the...
On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles
In this short survey, we would like to overview the recent development of the study on Deligne-Malgrange lattices and resolution of turning points for algebraic meromorphic flat bundles. We also explain their relation with wild harmonic bundles. The author hopes that it would be helpful for access to his work on wild harmonic bundles.
On Donaldson polynomials of rational ruled surfaces.
On -very ampleness of tensor products of ample line bundles on abelian surfaces
On K-spanned embeddings of projectiv manifolds.
On Picard bundles over Prym varieties.
On projective manifolds with nef anticanonical bundles.
On rank two vector bundles on an algebraic surface.
On reflexive sheaves with low sectional genera on threefolds.
On Reider's method for surfaces in positive characterstic.
On relative canonical sheaves of arithmetic surfaces.
On the 2 Very Ampleness of the Adjoint Bundle.
On the adjunction mapping for surfaces of Kodaira dimension ... 0 in Char.p.
On the adjunction theoretic classification of polarized varieties.
On the boundedness of the set of ample vector bundles with fixed sectional genus
On the Brill-Noether theory for K3 surfaces
Let (S, H) be a polarized K3 surface. We define Brill-Noether filtration on moduli spaces of vector bundles on S. Assume that (c 1(E), H) > 0 for a sheaf E in the moduli space. We give a formula for the expected dimension of the Brill-Noether subschemes. Following the classical theory for curves, we give a notion of Brill-Noether generic K3 surfaces. Studying correspondences between moduli spaces of coherent sheaves of different ranks on S, we prove our main theorem: polarized K3 surface which...
On the cohomological strata of families of vector bundles on algebraic surfaces
In this Note we study certain natural subsets of the cohomological stratification of the moduli spaces of rank vector bundles on an algebraic surface. In the last section we consider the following problem: take a bundle given by an extension, how can one recognize that is a certain given bundle? The most interesting case considered here is the case since it applies to the study of codimension meromorphic foliations with singularities on .