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A. Ramanathan 《Proceedings Mathematical Sciences》1996,106(4):421-449
We classify principal bundles on a compact Riemann surface. A moduli space for semistable principal bundles with a reductive
structure group is constructed using Mumford’s geometric invariant theory.
This is the second and concluding part of the thesis of late Professor A Ramanathan; the first part was published in the previous
issue. 相似文献
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Indranil Biswas 《Bulletin des Sciences Mathématiques》2010,134(7):747
Let X be a geometrically irreducible smooth projective curve defined over the real numbers. Let nX be the number of connected components of the locus of real points of X. Let x1,…,x? be real points from ? distinct components, with ?<nX. We prove that the divisor x1+?+x? is rigid. We also give a very simple proof of the Harnack's inequality. 相似文献
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Let X be a smooth projective hyperelliptic curve of arbitrary genus g. In this article, we will classify the rank 2 stable vector bundles with parabolic structure along a reduced divisor of degree 4. 相似文献
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In this article, we solve the problem of constructing moduli spaces of semistable principal bundles (and singular versions of them) over smooth projective varieties over algebraically closed ground fields of positive characteristic. 相似文献
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We give a geometric interpretation of the Weil representation of the metaplectic group, placing it in the framework of the geometric Langlands program.For a smooth projective curve X we introduce an algebraic stack of metaplectic bundles on X. It also has a local version , which is a gerbe over the affine Grassmanian of G. We define a categorical version of the (nonramified) Hecke algebra of the metaplectic group. This is a category of certain perverse sheaves on , which act on by Hecke operators. A version of the Satake equivalence is proved describing as a tensor category. Further, we construct a perverse sheaf on corresponding to the Weil representation and show that it is a Hecke eigen-sheaf with respect to . 相似文献
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Lucia Caporaso Cinzia Casagrande Maurizio Cornalba 《Transactions of the American Mathematical Society》2007,359(8):3733-3768
We treat the problem of completing the moduli space for roots of line bundles on curves. Special attention is devoted to higher spin curves within the universal Picard scheme. Two new different constructions, both using line bundles on nodal curves as boundary points, are carried out and compared with pre-existing ones.
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Gilberto Bini Claudio Fontanari 《Transactions of the American Mathematical Society》2006,358(7):3207-3217
Here we investigate some birational properties of two collections of moduli spaces, namely moduli spaces of (pointed) stable curves and of (pointed) spin curves. In particular, we focus on vanishings of Hodge numbers of type and on computations of Kodaira dimension. Our methods are purely algebro-geometric and rely on an induction argument on the number of marked points and the genus of the curves.
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The object of this paper is to study continuous vector bundles, over real algebraic varieties, admitting an algebraic structure. For large classes of real varieties, we obtain explicit information concerning the Grothendieck group of algebraic vector bundles. We show that in many cases this group is small compared to the corresponding group of continuous vector bundles. These results are used elsewhere to study the geometry of real algebraic varieties.Dedicated to Professor Alexander Grothendieck on the occasion of his 60th birthdaySupported by the NSF Grant DMS-8602672. 相似文献
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WINKELMANN Jrg 《中国科学 数学(英文版)》2011,(8)
We compare the behaviour of entire curves and integral sets,in particular in relation to locally trivial fiber bundles,algebraic groups and finite ramified covers over semi-abelian varieties. 相似文献
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We study complex vector bundles on a product of nonsingular real algebraic curves.
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Florent Schaffhauser 《Geometriae Dedicata》2011,151(1):187-206
A compact topological surface S, possibly non-orientable and with non-empty boundary, always admits a Klein surface structure (an atlas whose transition
maps are dianalytic). Its complex cover is, by definition, a compact Riemann surface M endowed with an anti-holomorphic involution which determines topologically the original surface S. In this paper, we compare dianalytic vector bundles over S and holomorphic vector bundles over M, devoting special attention to the implications that this has for moduli varieties of semistable vector bundles over M. We construct, starting from S, totally real, totally geodesic, Lagrangian submanifolds of moduli varieties of semistable vector bundles of fixed rank and
degree over M. This relates the present work to the constructions of Ho and Liu over non-orientable compact surfaces with empty boundary
(Ho and Liu in Commun Anal Geom 16(3):617–679, 2008). 相似文献