Moduli-stacks for bundles on semistable curves.
Monodromy of a class of logarithmic connections on an elliptic curve.
Multiple Bernoulli series, an Euler-MacLaurin formula, and Wall crossings
We study multiple Bernoulli series associated to a sequence of vectors generating a lattice in a vector space. The associated multiple Bernoulli series is a periodic and locally polynomial function, and we give an explicit formula (called wall crossing formula) comparing the polynomial densities in two adjacent domains of polynomiality separated by a hyperplane. We also present a formula in the spirit of Euler-MacLaurin formula. Finally, we give a decomposition formula for the Bernoulli series describing...
Multiplication of sections of stable vector bundles: the injectivity range.
Non-simple semistable vector bundles over a curve.
Non-simple vector bundles on curves.
On a class of partial -spreads of arising from scrolls.
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 cubics and quartics through a canonical curve
We construct families of quartic and cubic hypersurfaces through a canonical curve, which are parametrized by an open subset in a grassmannian and a Flag variety respectively. Using G. Kempf’s cohomological obstruction theory, we show that these families cut out the canonical curve and that the quartics are birational (via a blowing-up of a linear subspace) to quadric bundles over the projective plane, whose Steinerian curve equals the canonical curve
On Newstaed' s conjecture on vector bundles on algebraic curves.
On Picard bundles over Prym varieties.
On rank semistable vector bundles over an irreducible nodal curve of genus
Sia una curva irriducibile nodale di genere aritmetico . In queste note vogliamo mostrare come il sistema lineare delle quadriche, contenenti un opportuno modello proiettivo della curva, permette di descrivere i fibrati vettoriali semistabili, di rango , su .
On the Abel-Jacobi map for divisors of higher rank on a curve.
On The Brill-noether Theory of Spanned Vector Bundles on Smooth Curves
Here we study the integers (d, g, r) such that on a smooth projective curve of genus g there exists a rank r stable vector bundle with degree d and spanned by its global sections.
On the existence of curves in with stable normal bundle
We prove that for integers n,d,g such that n ≥ 4, g ≥ 2n and d ≥ 2g + 3n + 1, the general (smooth) curve C in with degree d and genus g has a stable normal bundle .
On the generalized theta divisor.
On the Gieseker-Petri Map for Rank 2 vector bundles.
On the motives of moduli of chains and Higgs bundles
We take another approach to Hitchin’s strategy of computing the cohomology of moduli spaces of Higgs bundles by localization with respect to the circle action. Our computation is done in the dimensional completion of the Grothendieck ring of varieties and starts by describing the classes of moduli stacks of chains rather than their coarse moduli spaces. As an application we show that the -torsion of the Jacobian acts trivially on the middle dimensional cohomology of the moduli space of twisted...
On the normal bundle of an exceptional curve in a higher dimensional algebraic manifold.
On the pole placement problem for linear systems of arbitrary genus.