Decomposable subbundles of polystable vector bundles on projective curves.
Degenerations of moduli of stable bundles over algebraic curves
Derived tubular algebras and APR-tilts
Differential operators and rank bundles over elliptic curves
Divisors on Mg,g+1 and the minimal resolution conjecture for points on canonical curves
Dynamics in the moduli space of Abelian differentials.
Effective divisors of higher rank on a curve and the Siegel formula
Equivariant vector bundles over affine subsets of the projective line
Exceptional linear systems on curves on Del Pezzo surfaces.
Existence of coherent systems of rank two and dimension four.
We show that the moduli space of coherent systems of rank two and dimension four on a generic curve of genus at least two is non-empty for any value of the parameter when the Brill-Noether number is at least one and the degree is odd or when the Brill-Noether number is at least ve and the degree is even. In all these cases there is one component of the moduli space of coherent systems of the expected dimension. The case of rank two and dimension four is particularly relevant as it is the rst case...
Factorisation of generalised theta functions. I.
Factorization of rank two theta functions. II. Proof of the Verlinde formula.
Faisceaux cohérents sur les courbes multiples.
This paper is devoted to the study of coherent sheaves on non reduced curves that can be locally embedded in smooth surfaces. If Y is such a curve then there is a filtration C ⊂ C2 ⊂ ... ⊂ Cn = Y such that C is the reduced curve associated to Y, and for very P ∈ C there exists z ∈ OY,P such that (zi) is the ideal of Ci in OY,P. We define, using canonical filtrations, new invariants of coherent sheaves on Y: the generalized rank and degree, and use them to state a Riemann-Roch theorem for sheaves...
Fibrés Vectoriels Semi-Stables sur une Courbe de Genre Deux et Association des Points dans L’espace Projectif
2000 Mathematics Subject Classification: 14D20, 14J60.The aim of this paper is to prove that a certain involution on the moduli space of stable bundles on a curve of genus two, can be viewed as a geometric operation on the corresponding set of points in projective space.
Fibrés vectoriels spéciaux
Fourier-Mukai transforms and stable bundles on elliptic curves.
Fragmented deformations of primitive multiple curves
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also a characterization...
Funtori integrali e fasci di Picard su varietà jacobiane e di Prym
Galois theory of -difference equations
Choose with . The main theme of this paper is the study of linear -difference equations over the field of germs of meromorphic functions at . A systematic treatment of classification and moduli is developed. It turns out that a difference module over induces in a functorial way a vector bundle on the Tate curve that was known for modules with ”integer slopes“, [Saul, 2]). As a corollary one rediscovers Atiyah’s classification of the indecomposable vector bundles on the complex Tate...
Gaussian maps and multiplication maps on certain projective varieties