相关论文: Stability and locally exact differentials on a cur…

We investigate sheaves supported on the zero section of the total space of a locally-free sheaf E on a smooth, projective variety X when the top exterior power of E is isomorphic to the canonical bundle of X. We rephrase this construction…

We give sufficient conditions for the (semi-)stability of torsion free sheaves on a primitive multiple curve. These conditions are used to prove that some moduli spaces of stable sheaves are not empty. We study mainly the quasi locally free…

We give a necessary and sufficient condition for the projectivisation of a slope semistable vector bundle to admit constant scalar curvature K\"ahler (cscK) metrics in adiabatic classes, when the base admits a constant scalar curvature…

In the last decades there have been introduced different concepts of stability for projective varieties. In this paper we give a natural and intrinsic criterion of the Chow, and Hilbert, stability for complex irreducible smooth projective…

Let $(E,\varphi)$ be decorated vector bundle of type $(a,b,c,N)$ on a smooth projective curve $X$. There is a suitable semistability condition for such objects which has to be checked for any weighted filtration of $E$. We prove, at least…

I show that on any smooth, projective ordinary curve of genus at least two and a projective embedding, there is a natural example of a stable Ulrich bundle for this embedding: namely the sheaf $B^1_X$ of locally exact differentials twisted…

Characteristic classes of oriented vector bundles can be identified with cohomology classes of the disjoint union of classifying spaces BSO_n of special orthogonal groups SO_n with n=0,1,... A characteristic class is stable if it extends to…

We study the stability of some homogeneous bundles on P^3 by using their representations of the quiver associated to the homgeneous bundles on P^3. In particular we show that homogeneous bundles on P^3 whose support of the quiver…

We prove that the discriminant of a nonsingular space curve of genus $g\geq 2$ is stable with respect to the standard action of the special linear group.

We prove a formula which relates Euler characteristic of moduli spaces of stable pairs on local K3 surfaces to counting invariants of semistable sheaves on them. Our formula generalizes Kawai-Yoshioka's formula for stable pairs with…

We present a novel notion of stable objects in a triangulated category. This Postnikov-stability is preserved by equivalences. We show that for the derived category of a projective variety this notion includes the case of semistable…

We consider slope stability of the canonical extension of the tangent bundle by the trivial line bundle and with the extension class c_1(T_X) on Picard-rank-1 Fano varieties. In cases where the index divides the dimension or the dimension…

We give the full answer to the question: on which curves the category of coherent sheaves $\Coh_{X}$ is tame. The answer is: these are just the curves from the list of Drozd-Greuel. Moreover, in this case the derived category…

We develop a theory of stable bundles and affine Hermitian-Einstein metrics for flat vector bundles over a special affine manifold (a manifold admitting an atlas whose gluing maps are all locally constant volume-preserving affine maps). Our…

We show that a principal G bundle on a smooth projective curve over a finite field is strongly semistable if and only if it is defined by a representation of the fundamental group scheme of the curve into G.

We use the theory of p-curvature of connections to analyze stable vector bundles of rank 2 on curves of genus 2 which pull back to unstable bundles under the Frobenius morphism. We take two approaches, first using explicit formulas for…

In this paper we show that the family of stable vector bundles gives a set of generators for the Chow ring, the K-theory and the derived category of any smooth projective variety.

Given a quasi-projective scheme M over complex numbers equipped with a perfect obstruction theory and a morphism to a nonsingular quasi-projective variety B, we show it is possible to find an affine bundle M'/ M that admits a perfect…

We study the dimension of loci of special line bundles on stable curves and for a fixed semistable multidegree. In case of total degree $d = g - 1$, we characterize when the effective locus gives a Theta divisor. In case of degree $g - 2$…

We prove that any vector bundle computing the rank-two Clifford index of a smooth projective algebraic curve is linearly semistable. We also identify conditions under which such bundles become linearly stable, thereby addressing a question…