On complex vector bundles on projective threefolds.
On congruences of lines in the projective space (Chapter 6 written in collaboration with M. Pedreira)
On connected divisors.
On contractions of extremal rays of Fano manifolds.
On covering and quasi-unsplit families of curves
Given a covering family of effective 1-cycles on a complex projective variety , we find conditions allowing one to construct a geometric quotient , with regular on the whole of , such that every fiber of is an equivalence class for the equivalence relation naturally defined by . Among other results, we show that on a normal and -factorial projective variety with canonical singularities and , every covering and quasi-unsplit family of rational curves generates a geometric extremal...
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 Deformations of Quintic Surfaces.
On Deformations of Threedimensional Rational Manifolds.
On degenerate secant varieties of secant defect two.
On del Pezzo fibrations
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 desingularized Horrocks-Mumford quintics.
On diagonal cubic surfaces.
On Donaldson polynomials of rational ruled surfaces.
On elementary transformations of ruled surfaces.
On Elliptic Surfaces in Characteristic p.
On Enriques Surfaces in Characteristic p. I.
On Enriques Surfaces in Characteristic p. II.
On Equisingular Deformations of Cone-Like Surface Singularities.
On equivalences of derived and singular categories
Let X and Y be two smooth Deligne-Mumford stacks and consider a pair of functions f: X → , g:Y → . Assuming that there exists a complex of sheaves on X × Y which induces an equivalence of D b(X) and D b(Y), we show that there is also an equivalence of the singular derived categories of the fibers f −1(0) and g −1(0). We apply this statement in the setting of McKay correspondence, and generalize a theorem of Orlov on the derived category of a Calabi-Yau hypersurface in a weighted projective...