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Surfaces kählériennes de volume fini et équations de Seiberg-Witten

Yann Rollin (2002)

Bulletin de la Société Mathématique de France

Soit M = ( ) une surface complexe réglée. Nous introduisons des métriques de volume fini sur M 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 M est équivalente à une condition de polystabilité parabolique sur  ; de plus ces métriques proviennent toutes de quotients...

SUX(r, L) is separably unirational

Georg Hein (2009)

Open Mathematics

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.

Symplectic structures on moduli spaces of framed sheaves on surfaces

Francesco Sala (2012)

Open Mathematics

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.

Tensor product theorem for Hitchin pairs – An algebraic approach

V. Balaji, A.J. Parameswaran (2011)

Annales de l’institut Fourier

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 p , with p satisfying some natural bounds. We also prove the corresponding theorem for polystable Hitchin pairs.

The automorphism group of M ¯ 0 , n

Andrea Bruno, Massimiliano Mella (2013)

Journal of the European Mathematical Society

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 M ¯ 0 , n is the permutation group on n elements as soon as n 5 .

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