Surface bundles over surfaces of small genus.
Soit une surface complexe réglée. Nous introduisons des métriques de volume fini sur dons les singularités sont paramétrisées par une structure parabolique sur le fibré . Nous généralisons alors un résultat de Burns-deBartolomeis et Le Brun, en montrant que l’existence de métriques kählériennes singulières, de volume fini, à courbure scalaire constante négative ou nulle sur est équivalente à une condition de polystabilité parabolique sur ; de plus ces métriques proviennent toutes de quotients...
We show that the moduli space of SUX (r, L) of rank r bundles of fixed determinant L on a smooth projective curve X is separably unirational.
We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a symplectic structure on the moduli spaces of framed sheaves on some birationally ruled surfaces.
We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields of characteristic zero and characteristic , with satisfying some natural bounds. We also prove the corresponding theorem for polystable Hitchin pairs.
The paper studies fiber type morphisms between moduli spaces of pointed rational curves. Via Kapranov’s description we are able to prove that the only such morphisms are forgetful maps. This allows us to show that the automorphism group of is the permutation group on elements as soon as .