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1.
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
2.
Francesco Bottacin 《Mathematische Zeitschrift》2000,233(2):219-250
Let X be a smooth n-dimensional projective variety defined over and let L be a line bundle on X. In this paper we shall construct a moduli space parametrizing -cohomology L-twisted Higgs pairs, i.e., pairs where E is a vector bundle on X and . If we take , the canonical line bundle on X, the variety is canonically identified with the cotangent bundle of the smooth locus of the moduli space of stable vector bundles on X and, as such, it has a canonical symplectic structure. We prove that, in the general case, in correspondence to the choice
of a non-zero section , one can define, in a natural way, a Poisson structure on . We also analyze the relations between this Poisson structure on and the canonical symplectic structure of the cotangent bundle to the smooth locus of the moduli space of parabolic bundles
over X, with parabolic structure over the divisor D defined by the section s. These results generalize to the higher dimensional case similar results proved in [Bo1] in the case of curves.
Received November 4, 1997; in final form May 28, 1998 相似文献
3.
We describe the moduli spaceM
1 (c
2) of 't Hooft bundles onP
3, that is instanton bundles having sections at the first twist. We prove that such a moduli space is a rational variety whose
singular locus is the moduli space of special 't Hooft bundles studied in [HN]. It turns out thatM
1 (c
2) possesses a canonical desingularization provided by the projectivized of a vector bundle on the Hilbert schemeH of the space curves which correspond to 't Hooft bundles in the Serre construction. Moreover, we show that the connected
components of such curves are lines or multiple lines, which are scheme-theoretically a product. On such multiple lines every
vector bundle splits, and we are able to determine their normal bundle. This allows to reprove the smoothness ofH, already known from [C], and the smoothness ofM
1, shown in [C] and [NT].
Sunto Si descrive lo spazio dei moduliM 1 (c 2) dei fibrati vettoriali di 't Hooft suP 3, cioè dei fibrati istantoni che ammettono una sezione lineare. Si dimostra che tale spazio è una varietà razionale il cui luogo singolare è costituito dai fibrati di 't Hooft speciali studiati in [HN]. Si trova, inoltre, una desingolarizzazione diM 1 (c 2) data da un aperto di un fibrato proiettivo sullo schema di Hilbert delle curve che sono luoghi degli zeri di sezioni lineari di fibrati di 't Hooft. Le componenti connesse di tali curve sono rette o rette multiple isomorfe a un prodotto. Questo risultato è conseguenza del fatto che ogni retta multiplaZ di genere aritmeticop a (Z)≤1—deg (Z) fibrata in punti multipli curvilinei è schematicamente isomorfa al multiplo di una sezione di una opportuna superficie rigata razionale.相似文献
4.
Symplectic instanton vector bundles on the projective space ℙ3 constitute a natural generalization of mathematical instantons of rank-2. We study the moduli space I n;r of rank-2r symplectic instanton vector bundles on ℙ3 with r ≥ 2 and second Chern class n ≥ r, n ≡ r (mod 2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus I n;r * of tame symplectic instantons is irreducible and has the expected dimension, equal to 4n(r + 1) −r(2r + 1). 相似文献
5.
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
6.
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
7.
In [K2] Moishezon twistor spaces over the connected sum (), which do not contain effective divisors of degree one, were constructed as deformations of the twistor spaces introduced
in [LeB]. We study their structure for by constructing a modification which is a conic bundle over . We show that they are rational. In case n = 4 we give explicit equations for such conic bundles and use them to construct explicit birational maps between these conic
bundles and .
Received October 8, 1996; in final form May 16, 1997 相似文献
8.
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
9.
Let F be a finite field of characteristic not 2, and SF a subset with three elements. Consider the collectionThen (F,S) is a simple 2-design and the parameter λ of (F,S) is 1, 2, 3 or 6. We find in this paper the full automorphism group of (F,S). Namely, if we put U={r | {0,1,r}S} and K the subfield of F generated by U, then the automorphisms of (F,S) are the maps of the form xg(α(x))+b, xF, where bF, α : F→F is a field automorphism fixing U, and g is a linear transformation of F considered as a vector space over K. 相似文献
S={S·a+b | a,bF, a≠0}.
10.
This paper gives a construction of the moduli space of framed parabolic sheaves on a Riemann surface. This space serves as
a universal, master, space for the well known moduli space of parabolic bundles, as well as moduli spaces of vector bundles,
which can all be obtained from this space by torus quotients. The construction is given for the structure group SL(N, C), and indeed is adapted to this case. At the end of the paper, an approach is suggested for dealing with the case of arbitrary
reductive groups, involving the associated loop group. 相似文献
11.
Fix a holomorphic line bundle ξ over a compact connected Riemann surface X of genus g, with g?2, and also fix an integer r such that degree(ξ)>r(2g−1). Let Mξ(r) denote the moduli space of stable vector bundles over X of rank r and determinant ξ. The Fourier-Mukai transform, with respect to a Poincaré line bundle on X×J(X), of any F∈Mξ(r) is a stable vector bundle on J(X). This gives an injective map of Mξ(r) in a moduli space associated to J(X). If g=2, then Mξ(r) becomes a Lagrangian subscheme. 相似文献
12.
We construct a holomorphic Hermitian line bundle over the moduli space of stable triples of the form (E1, E2,?), where E1 and E2 are holomorphic vector bundles over a fixed compact Riemann surfaceX, and?: E2 → E1 is a holomorphic vector bundle homomorphism. The curvature of the Chern connection of this holomorphic Hermitian line bundle is computed. The curvature is shown to coincide with a constant scalar multiple of the natural Kähler form on the moduli space. The construction is based on a result of Quillen on the determinant line bundle over the space of Dolbeault operators on a fixed C∞ Hermitian vector bundle over a compact Riemann surface. 相似文献
13.
We introduce and study the Prym vector bundle P of holomorphic Prym differentials and the Ganning cohomology bundle G over the Teichmueller space of compact Riemann surfaces of genus g2 and over the Torelli space of genus g2. We construct a basis of holomorphic Prym differentials on a variable compact Riemann surface which depends on the moduli of the compact Riemann surface and on the essential characters. From these bundles we compose an exact sequence of holomorphic vector bundles over the product of the Teichmueller space of genus g and a special domain in the complex manifold C
2g/Z
2g. 相似文献
14.
R.J Plymen 《Journal of Functional Analysis》1982,49(2):186-197
Let F be a symplectic vector bundle over a space X. We construct a bundle of elementary C1-algebras over X, and prove that the Dixmier-Douady invariant of this bundle is zero. The underlying Hilbert bundles, with their associated module structures, determine a characteristic class: we prove that this class is the second Stiefel-Whitney class of F. 相似文献
15.
Indranil Biswas 《Annals of Global Analysis and Geometry》2011,40(1):85-94
In Biswas and Raghavendra (Proc Indian Acad Sci (Math Sci) 103:41–71, 1993; Asian J Math 2:303–324, 1998), a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian
structure on it. The construction of the Hermitian structure was indirect: The parabolic determinant line bundle was identified
with the pullback of the determinant line bundle on a moduli space of usual vector bundles over a covering curve. The Hermitian
structure on the parabolic determinant bundle was taken to be the pullback of the Quillen metric on the determinant line bundle
on the moduli space of usual vector bundles. Here a direct construction of the Hermitian structure is given. For that we need
to establish a version of the correspondence between the stable parabolic bundles and the Hermitian–Einstein connections in
the context of conical metrics. Also, a recently obtained parabolic analog of Faltings’ criterion of semistability plays a
crucial role. 相似文献
16.
Rui Albuquerque 《Annali di Matematica Pura ed Applicata》2009,188(3):429-443
We consider some classical fibre bundles furnished with almost complex structures of twistor type, deduce their integrability
in some cases and study self-holomorphic sections of the general twistor space, with which we define a new moduli space of complex structures. We also recall the
theory of flag manifolds to study the Siegel domain and other domains alike, which are the fibres of various symplectic twistor
spaces. We prove that they are all Stein. In the context of a Riemann surface, with its canonical symplectic-metric connection
and local structure equations, the moduli space is studied again. 相似文献
17.
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
18.
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line ℂ, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing
new asymptotic invariants. We show that the underlying holomorphic bundle extends to T×ℙ1. The converse statement is also true, namely a holomorphic bundle on T×ℙ1 which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton. Finally,
we study the hyperk?hler geometry of the moduli space of doubly-periodic instantons, and prove that the Nahm transform previously
defined by the second author is a hyperk?hler isometry with the moduli space of certain meromorphic Higgs bundles on the dual
torus.
Received June 8, 2000 / final version received February 1, 2001?Published online April 3, 2001 相似文献
19.
Indranil Biswas Amit Hogadi Yogish I. Holla 《Central European Journal of Mathematics》2012,10(4):1300-1305
Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic
zero. For a fixed line bundle L on C, let M
C
(r; L) be the coarse moduli space of semistable vector bundles E over C of rank r with ∧
r
E = L. We show that the Brauer group of any desingularization of M
C
(r; L) is trivial. 相似文献
20.
Edoardo Ballico 《Journal of Pure and Applied Algebra》2005,195(1):7-19
Let S be a ruled surface inside a smooth threefold W and let E be a vector bundle on a formal neighborhood of S. We find minimal conditions under which the local moduli space of E is finite dimensional and smooth. Moreover, we show that E is a flat limit of a flat family of vector bundles whose general element we describe explicitly. 相似文献