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1.
LetY be a smooth projective curve degenerating to a reducible curveX with two components meeting transversally at one point. We show that the moduli space of vector bundles of rank two and odd determinant on Ydegenerates to a moduli space onX which has nice properties, in particular, it has normal crossings. We also show that a nice degeneration exists when we fix the determinant. We give some conjectures concerning the degeneration of moduli space of vector bundles onY with fixed determinant and arbitrary rank. 相似文献
2.
S. A. Kuleshov 《Mathematical Notes》1997,62(6):707-725
We investigate the relation between stable representations of quivers and stable sheaves. A construction of thin smooth compact
moduli spaces for stable sheaves on quadrics based on this relation is presented.
Translated fromMatematicheskie Zametki, Vol 62, No. 6, pp. 843–864, December, 1997
Translated by S. K. Lando 相似文献
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Sambaiah Kilaru 《Proceedings Mathematical Sciences》1998,108(3):217-226
We identify the spaces Homi(ℙ1,M) fori = 1, 2, whereM is the moduli space of vector bundles of rank 2 and determinant isomorphic to
,x
0 ∈X, on a compact Riemann surface of genusg ≥ 2. 相似文献
5.
Mario Maican 《代数通讯》2017,45(1):332-342
We find certain relations between flag Hilbert schemes of points on plane curves and moduli spaces of one-dimensional plane sheaves. We show that some of these moduli spaces are stably rational. 相似文献
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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
10.
Montserrat Teixidor i Bigas 《Mathematische Annalen》1991,290(1):341-348
Partially supported by my husband during the preparation of this work 相似文献
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For a compact, connected Lie group G, we study the moduli of pairs (Σ,E), where Σ is a genus g Riemann surface and E→Σ is a flat G-bundle. Varying both the Riemann surface Σ and the flat bundle leads to a moduli space , parametrizing families Riemann surfaces with flat G-bundles. We show that there is a stable range in which the homology of is independent of g. The stable range depends on the genus of the surface. We then identify the homology of this moduli space in the stable range, in terms of the homology of an explicit infinite loop space. Rationally, the stable cohomology of this moduli space is generated by the Mumford-Morita-Miller κ-classes, and the ring of characteristic classes of principal G-bundles, H∗(BG). Equivalently, our theorem calculates the homology of the moduli space of semi-stable holomorphic bundles on Riemann surfaces.We then identify the homotopy type of the category of one-manifolds and surface cobordisms, each equipped with a flat G-bundle. Our methods combine the classical techniques of Atiyah and Bott, with the new techniques coming out of Madsen and Weiss's proof of Mumford's conjecture on the stable cohomology of the moduli space of Riemann surfaces. 相似文献
14.
Joseph P. Previte Eugene Z. Xia 《Transactions of the American Mathematical Society》2002,354(6):2475-2494
Let be an orientable genus 0$"> surface with boundary . Let be the mapping class group of fixing . The group acts on the space of -gauge equivalence classes of flat -connections on with fixed holonomy on . We study the topological dynamics of the -action and give conditions for the individual -orbits to be dense in .
15.
We prove that the moduli spaces
of polarized Abelian threefolds with polarizations of types D=(1,1,2),(1,2,2),(1,1,3) or (1,3,3) are unirational. The result is based on the study of families of simple coverings of elliptic curves of degree 2 or 3 and on the study of the corresponding period mappings associated with holomorphic differentials with trace 0. In particular we prove the unirationality of the Hurwitz space
which parametrizes simply branched triple coverings of an elliptic curve Y with determinants of the Tschirnhausen modules isomorphic to A-1. Dedicated to the memory of Fabio BardelliMathematics Subject Classification (2000) Primary: 14K10; Secondary: 14H10, 14H30, 14D07 相似文献
16.
Kieran G. O'Grady 《Inventiones Mathematicae》1993,112(1):585-613
Oblatum 14-III-1992 & 16-XI-1992 相似文献
17.
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
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19.
Let X be a smooth algebraic surface, L ? Pic(X) L \in \textrm{Pic}(X) and H an ample divisor on X. Set MX,H(2; L, c2) the moduli space of rank 2, H-stable vector bundles F on X with det(F) = L and c2(F) = c2. In this paper, we show that the geometry of X and of MX,H(2; L, c2) are closely related. More precisely, we prove that for any ample divisor H on X and any L ? Pic(X) L \in \textrm{Pic}(X) , there exists
n0 ? \mathbbZ n_0 \in \mathbb{Z} such that for all
n0 \leqq c2 ? \mathbbZ n_0 \leqq c_2 \in \mathbb{Z} , MX,H(2; L, c2) is rational if and only if X is rational. 相似文献
20.
Let (X,D) be an ?-pointed compact Riemann surface of genus at least two. For each point x∈D, fix parabolic weights such that . Fix a holomorphic line bundle ξ over X of degree one. Let PMξ denote the moduli space of stable parabolic vector bundles, of rank two and determinant ξ, with parabolic structure over D and parabolic weights . The group of order two line bundles over X acts on PMξ by the rule E∗⊗L?E∗⊗L. We compute the Chen-Ruan cohomology ring of the corresponding orbifold. 相似文献