Degenerations of moduli of stable bundles over algebraic curves
Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space
The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.
Deux composantes du bord de
Nous étudions deux nouvelles composantes irréductibles du bord de la variété des instantons de degré 3. Nous décrivons grâce aux transformations cubo-cubiques involutives déduites de la monade de Beilinson (ce sont des transformations de Cremona particulières). Nous exhibons alors les deux composantes du bord par dégénérescence sur les transformations. Nous mettons en évidence la dualité qui les lie : les transformations cubo-cubiques de l’une sont les inverses de l’autre. Nous décrivons en...
Die Modulräume 3MstIP3 (?2,3,c3) .
Die Singularitäten der Modulmannigfaltigkeit ...(n) der stabilen Kurven vom Geschlecht g...2 mit n-Teilungspunktstruktur.
Diffeomorphism types of elliptic surfaces with pg=1.
Divisor classes associated to families of stable varieties, with applications to the moduli space of curves
Eine Bemerkung zu einer Arbeit von P. E. Newstead.
Eine Klassenzahlformel für singuläre Moduln der Picardschen Modulgruppen
Einige Beispiele nichtalgebraischer Singularitäten.
Einschränkung stabiler Vektorraumbündel vom Rang 3 Hyperebenen des projectiven Raumes.
Errata-Corrige : “Canonical surfaces with and ”
Erratum to : Morphisms, line bundles and moduli spaces in real algebraic geometry
Everywhere non reduced moduli spaces.
Explicit resolution of local singularities of moduli-spaces.
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...
Families of linear differential equations related to the second Painlevé equation
This paper is a sequel to [vdP-Sa] and [vdP]. The two classes of differential modules (0,-,3/2) and (-,-,3), related to PII, are interpreted as fine moduli spaces. It is shown that these moduli spaces coincide with the Okamoto-Painlevé spaces for the given parameters. The geometry of the moduli spaces leads to a proof of the Painlevé property for PII in standard form and in the Flaschka-Newell form. The Bäcklund transformations, the rational solutions and the Riccati solutions for PII are derived...
Familles de fibrés vectoriels sur une surface de Riemann
Familles de revêtements de la droite projective