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1.
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
2.
3.
Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli scheme of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 (with determinant equal to a theta characteristic) whose Frobenius pull-back is not semi-stable. The indeterminacy of the Frobenius map at this point can be resolved by introducing Higgs bundles. 相似文献
4.
In this work, using elementary transformations and prioritary sheaves, we establish birational maps between certain moduli spaces of stable vector bundles over 2 with the same rank and different Chern classes. As an application we give a simple proof of the rationality of the moduli spaces M(r; c
1, c
2) of rank r stable vector bundles over 2 with given Chern classes for a huge families of the triples (r; c
1, c
2).Partially supported by BFM2001-3584
Mathematics Subject Classification (2000):Primary 14D20, 14D05; Secondary 14F05 相似文献
5.
Francesco Bottacin 《Mathematische Nachrichten》2000,220(1):33-44
In this paper we prove that the moduli spaces of framed vector bundles over a surface X, satisfying certain conditions, admit a family of Poisson structures parametrized by the global sections of a certain line bundle on X. This generalizes to the case of framed vector bundles previous results obtained in [B2] for the moduli space of vector bundles over a Poisson surface. As a corollary of this result we prove that the moduli spaces of framed SU(r) – instantons on S4 = ℝ4 ∪ {∞} admit a natural holomorphic symplectic structure. 相似文献
6.
Dimitri Markushevich Alexander S. Tikhomirov Günther Trautmann 《Central European Journal of Mathematics》2012,10(4):1331-1355
We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector bundles on
trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundles and connections
in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according to a
result of Kollár. As an example, the compactification of the space of stable rank 2 vector bundles with Chern classes c
1 = 0, c
1 = 2 on the projective plane is studied in more detail. Proofs are only indicated and will appear in separate papers. 相似文献
7.
The presentation of the quantum cohomology of the moduli spaceof stable vector bundles of rank two and odd degree with fixeddeterminant over a Riemann surface of genus g > 2 is obtained.The argument avoids the use of gauge theory, providing an alternativeproof to that given by the author in Duke Math. J. 98 (1999)525540. 2000 Mathematics Subject Classification 14N35(primary); 14H60, 53D45 (secondary). 相似文献
8.
Let G be a reductive group over an algebraically closed field k. Consider the moduli space of stable principal G-bundles on a smooth projective curve C over k. We give necessary and sufficient conditions for the existence of Poincaré bundles over open subsets of this moduli space,
and compute the orders of the corresponding obstruction classes. This generalizes the previous results of Newstead, Ramanan
and Balaji–Biswas–Nagaraj–Newstead to all reductive groups, to all topological types of bundles, and also to all characteristics. 相似文献
9.
The cohomology ring of the moduli space of stable holomorphicvector bundles of rank n and degree d over a Riemann surfaceof genus g > 1 has a standard set of generators when n andd are coprime. When n = 2 the relations between these generatorsare well understood, and in particular a conjecture of Mumford,that a certain set of relations is a complete set, is knownto be true. In this article generalisations are given of Mumford'srelations to the cases when n > 2 and also when the bundlesare parabolic bundles, and these are shown to form completesets of relations. 2000 Mathematics Subject Classification 14H60. 相似文献
10.
Indranil Biswas 《Journal of Pure and Applied Algebra》2008,212(10):2298-2306
We study certain moduli spaces of stable vector bundles of rank 2 on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing intermediate cohomology. In one case, all except one component of the moduli space has such vector bundles. 相似文献
11.
Nitin Nitsure 《Proceedings Mathematical Sciences》1986,95(1):61-77
The purpose of this paper is to compute the Betti numbers of the moduli space ofparabolic vector bundles on a curve (see Seshadri [7], [8] and Mehta & Seshadri [4]), in the case where every semi-stable parabolic bundle is necessarily
stable. We do this by generalizing the method of Atiyah and Bott [1] in the case of moduli of ordinary vector bundles. Recall
that (see Seshadri [7]) the underlying topological space of the moduli of parabolic vector bundles is the space of equivalence
classes of certain unitary representations of a discrete subgroup Γ which is a lattice in PSL (2,R). (The lattice Γ need not necessarily be co-compact).
While the structure of the proof is essentially the same as that of Atiyah and Bott, there are some difficulties of a technical
nature in the parabolic case. For instance the Harder-Narasimhan stratification has to be further refined in order to get
the connected strata. These connected strata turn out to have different codimensions even when they are part of the same Harder-Narasimhan
strata.
If in addition to ‘stable = semistable’ the rank and degree are coprime, then the moduli space turns out to be torsion-free
in its cohomology.
The arrangement of the paper is as follows. In § 1 we prove the necessary basic results about algebraic families of parabolic
bundles. These are generalizations of the corresponding results proved by Shatz [9]. Following this, in § 2 we generalize
the analytical part of the argument of Atiyah and Bott (§ 14 of [1]). Finally in § 3 we show how to obtain an inductive formula
for the Betti numbers of the moduli space. We illustrate our method by computing explicitly the Betti numbers in the special
case of rank = 2, and one parabolic point. 相似文献
12.
We determine all of lines in the moduli space M of stable bundles for arbitrary rank and degree. A further application of minimal rational curves is also given in last section.
This work was supported by the Competitive Earmarked Research Grant (Grant No. HKU7025/03P) of the Research Grant Council,
Hong Kong 相似文献
13.
14.
Lin Weng 《Mathematische Annalen》2001,320(2):239-283
In Part I, Deligne-Riemann-Roch isometry is generalized for punctured Riemann surfaces equipped with quasi-hyperbolic metrics.
This is achieved by proving the Mean Value Lemmas, which explicitly explain how metrized Deligne pairings for -admissible metrized line bundles depend on . In Part II, we first introduce several line bundles over Knudsen-Deligne-Mumford compactification of the moduli space (or
rather the algebraic stack) of stable N-pointed algebraic curves of genus g, which are rather natural and include Weil-Petersson, Takhtajan-Zograf and logarithmic Mumford line bundles. Then we use
Deligne-Riemann-Roch isomorphism and its metrized version (proved in Part I) to establish some fundamental relations among
these line bundles. Finally, we compute first Chern forms of the metrized Weil-Petersson, Takhtajan-Zograf and logarithmic
Mumford line bundles by using results of Wolpert and Takhtajan-Zograf, and show that the so-called Takhtajan-Zograf metric
on the moduli space is algebraic.
Received February 14, 2000 / Accepted August 18, 2000 / Published online February 5, 2001 相似文献
15.
We define complexes of vector bundles on products of moduli spaces of framed rank r torsion-free sheaves on
\mathbbP2{\mathbb{P}^2} . The top non-vanishing equivariant Chern classes of the cohomology of these complexes yield actions of the r-colored Heisenberg and Clifford algebras on the equivariant cohomology of the moduli spaces. In this way we obtain a geometric
realization of the boson-fermion correspondence and related vertex operators. 相似文献
16.
Sergey Mozgovoy 《manuscripta mathematica》2010,131(1-2):63-86
Given a curve over a finite field, we compute the number of stable bundles of not necessarily coprime rank and degree over it. We apply this result to compute the virtual Poincaré polynomials of the moduli spaces of stable bundles over a curve. A similar formula for the virtual Hodge polynomials and motives is conjectured. 相似文献
17.
Young-Hoon Kiem 《Transactions of the American Mathematical Society》2003,355(5):1843-1856
We compute the stringy E-function (or the motivic integral) of the moduli space of rank 2 bundles over a Riemann surface of genus 3. In doing so, we answer a question of Batyrev about the stringy E-functions of the GIT quotients of linear representations.
18.
Georg Hein 《Central European Journal of Mathematics》2009,7(1):59-60
We show that the moduli space of SU
X
(r, L) of rank r bundles of fixed determinant L on a smooth projective curve X is separably unirational.
相似文献
19.
Andreas Matuschke 《Mathematische Nachrichten》2000,211(1):109-126
We consider a compact twistor space P and assume that there is a surface S ⊂ P, which has degree one on twistor fibres and contains a twistor fibre F, e.g. P a LeBrun twistor space ([20], [18]). Similar to [6] and [5] we examine the restriction of an instanton bundle V equipped with a fixed trivialization along F to a framed vector bundle over (S, F). First we develope inspired by [13] a suitable deformation theory for vector bundles over an analytic space framed by a vector bundle over a subspace of arbitrary codimension. In the second section we describe the restriction as a smooth natural transformation into a fine moduli space. By considering framed U(r)‐instanton bundles as a real structure on framed instanton bundles over P, we show that the bijection between isomorphism classes of framed U(r)‐instanton bundles and isomorphism classes of framed vector bundles over (S, F) due to [5] is actually an isomorphism of moduli spaces. 相似文献
20.
We give an algebro-geometric derivation of the known intersection theory on the moduli space of stable rank 2 bundles of odd degree over a smooth curve of genus g. We lift the computation from the moduli space to a Quot scheme, where we obtain the intersections via equivariant localization with respect to a natural torus action. 相似文献