On the rationality of certain strata of the Lange stratification of stable vector bundles on curves.
On the rationality of the moduli schemes of vector bundles on curves
On the space curves with the same dual varietey.
On the stability of the restricted bundle of space curves contained in a quartic surface.
Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface (II).
In [6], orbifold G-bundles on a certain class of elliptic fibrations over a smooth complex projective curve X were related to parabolic G-bundles over X. In this continuation of [6] we define and investigate holomorphic connections on an orbifold G-bundle over an elliptic fibration.
Orthogonal bundles on curves and theta functions
Let be the moduli space of principal -bundles on a curve , and the determinant bundle on . We define an isomorphism of onto the dual of the space of -th order theta functions on the Jacobian of . This isomorphism identifies the rational map defined by the linear system with the map which associates to a quadratic bundle the theta divisor . The two components and of are mapped into the subspaces of even and odd theta functions respectively. Finally we discuss the analogous...
Parabolic bundles, elliptic surfaces and SU (2)-representation spaces of genus zero Fuchsian groups.
Periods of harmonic Prym differentials on a compact Riemann surface.
Polarizations of Prym varieties for Weyl groups via abelianization
Let be a Galois covering of smooth projective curves with Galois group the Weyl group of a simple and simply connected Lie group . For any dominant weight consider the curve . The Kanev correspondence defines an abelian subvariety of the Jacobian of . We compute the type of the polarization of the restriction of the canonical principal polarization of to in some cases. In particular, in the case of the group we obtain families of Prym-Tyurin varieties. The main idea is the use of...
Problème de Brill-Noether pour les fibrés de Steiner. Applications aux courbes gauches
Pryum varieties and the Verlinde formula.
Quasi-tilted algebras of canonical type
Quivers, vector bundles and coverings of smooth curves.
Rank additivity for quasi-tilted algebras of canonical type
Given the category of coherent sheaves over a weighted projective line (of any representation type), the endomorphism ring of an arbitrary tilting sheaf - which is by definition an almost concealed canonical algebra - is shown to satisfy a rank additivity property (Theorem 3.2). Moreover, this property extends to the representationinfinite quasi-tilted algebras of canonical type (Theorem 4.2). Finally, it is demonstrated that rank additivity does not generalize to the case of tilting complexes...
Rank two Ulrich modules over the affine cone of the simple node.
Recent results on quiver sheaves
In this article, we survey recent work on the construction and geometry of representations of a quiver in the category of coherent sheaves on a projective algebraic manifold. We will also prove new results in the case of the quiver • ← • → •.
Representations of the fundamental group and vector bundles.
Restriction of stable bundles on a Jacobian of genus 2 to an embedded curve.
Roots of Nakayama and Auslander-Reiten translations
We discuss the roots of the Nakayama and Auslander-Reiten translations in the derived category of coherent sheaves over a weighted projective line. As an application we derive some new results on the structure of selfinjective algebras of canonical type.
Ropes on a line embedded in a Grassmannian variety.