On 0-dimensional complete intersections.
On 2-Spannedness for the adjunction mapping.
On a birational classification of bundles and reflexive sheaves on surfaces
On a certain generalization of spherical twists
This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of -curves on threefolds, or deforming -objects introduced by D.Huybrechts and R.Thomas.
On a geometric property of the normal bundle of surfaces in IP4.
On a spanned tautological bundle.
On algebraic curves.
On Ample and spanned Rank-3 Bundles with Low Chern numbers.
On ample and spanned vector bundles with zero ...-genera.
On Bănică sheaves and Fano manifolds
On Barth's restriction theorem.
On Buchsbaum bundles on quadric hypersurfaces
Let E be an indecomposable rank two vector bundle on the projective space ℙn, n ≥ 3, over an algebraically closed field of characteristic zero. It is well known that E is arithmetically Buchsbaum if and only if n = 3 and E is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically Buchsbaum vector bundles on the smooth quadric hypersurface Q n ⊂ ℙn+1, n ≥ 3. We give in fact a full classification and prove that n must be at most...
On Clifford's theorem for rank-3 bundles.
In this paper we obtain bounds on h0(E) where E is a semistable bundle of rank 3 over a smooth irreducible projective curve X of genus g ≥ 2 defined over an algebraically closed field of characteristic 0. These bounds are expressed in terms of the degrees of stability s1(E), s2(E). We show also that in some cases the bounds are best possible. These results extend recent work of J. Cilleruelo and I. Sols for bundles of rank 2.
On complex vector bundles on projective threefolds.
On compositions and triality.
On desingularized Horrocks-Mumford quintics.
On Donaldson polynomials of rational ruled surfaces.
On generation of jets for vector bundles.
We introduce and study the k-jet ampleness and the k-jet spannedness for a vector bundle, E, on a projective manifold. We obtain different characterizations of projective space in terms of such positivity properties for E. We compare the 1-jet ampleness with different notions of very ampleness in the literature.
On Harder-Narashimhan stratification over Quot schemes.
On -very ampleness of tensor products of ample line bundles on abelian surfaces