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1.
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
2.
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
3.
4.
5.
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
6.
7.
8.
LetX
0 be a projective curve whose singularity is one ordinary double point. We construct a birational modelG(n, d) of the moduli spaceU(n, d) of stable torsion free sheaves in the case (n, d)= 1, such that G(n, d) has normal crossing singularities and behaves well under specialization i.e. if a smooth projective curve specializes toX
0, then the moduli space of stable vector bundles of rankn and degreed onX specializes toG(n, d). This generalizes an earlier work of Gieseker in the rank two case. 相似文献
9.
Kieran G. O'Grady 《Inventiones Mathematicae》1993,112(1):585-613
Oblatum 14-III-1992 & 16-XI-1992 相似文献
10.
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
11.
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
12.
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
13.
Let X be a real form of a Hirzebruch surface. Let M H (r,c 1, c 2) be the moduli space of vector bundles on X. Under some numerical conditions on r, c 1 and c 2, we identify those M H (r,c 1,c 2) that are rational. 相似文献
14.
15.
Rosa M. Miro-Roig 《manuscripta mathematica》1993,79(1):391-402
Partially supported by DGICYT PB88-0224 相似文献
16.
Horrocks has shown that every vector bundle on 2 and 3 admits a certain double-ended resolution by line bundles, which he called a monad. We reprove Horrocks' results taking much care of uniqueness of the monads so obtained. This technique should be useful for constructing moduli spaces of stable vector bundles. 相似文献
17.
We compute the rational Betti cohomology groups of the coarse moduli spaces of geometrically marked Del Pezzo surfaces of degree 3 and 4 as representations of the Weyl groups of the corresponding root systems. The proof uses a blend of methods from point counting over finite fields and techniques from arrangement complements. 相似文献
18.
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
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20.
P. E. Newstead 《Mathematische Annalen》1975,215(3):251-268