共查询到20条相似文献,搜索用时 381 毫秒
1.
For moduli space of stable parabolic bundles on a compact Riemann surface, we derive an explicit formula for the curvature of its canonical line bundle with respect to Quillen’s metric and interprete it as a local index theorem for the family of \(\overline\partial\)-operators in the associated parabolic endomorphism bundles. The formula consists of two terms: one standard (proportional to the canonical Kähler form on the moduli space), and one nonstandard, called a cuspidal defect, that is defined by means of special values of the Eisenstein–Maass series. The cuspidal defect is explicitly expressed through the curvature forms of certain natural line bundles on the moduli space related to the parabolic structure. We also compare our result with Witten’s volume computation. 相似文献
2.
We study moduli of vector bundles on a two-dimensional neighbourhood Z k of an irreducible curve ? ? ?1 with ?2 = ?k and give an explicit construction of their moduli stacks. For the case of instanton bundles, we stratify the stacks and construct moduli spaces. We give sharp bounds for the local holomorphic Euler characteristic of bundles on Z k and prove existence of families of bundles with prescribed numerical invariants. Our numerical calculations are performed using a Macaulay 2 algorithm, which is available for download at http://www.maths.ed.ac.uk/~s0571100/Instanton/. 相似文献
3.
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
4.
Mihnea Popa 《Transactions of the American Mathematical Society》2002,354(5):1869-1898
In this paper we approach the study of generalized theta linear series on moduli of vector bundles on curves via vector bundle techniques on abelian varieties.
We study a naturally defined class of vector bundles on a Jacobian, called Verlinde bundles, in order to obtain information about duality between theta functions and effective global and normal generation on these moduli spaces.
5.
The aim of this paper is to construct the parabolic version of the Donaldson-Uhlenbeck compactification for the moduli space
of parabolic stable bundles on an algebraic surface with parabolic structures along a divisor with normal crossing singularities.
We prove the non-emptiness of the moduli space of parabolic stable bundles of rank 2. 相似文献
6.
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
7.
8.
A Ramanathan 《Proceedings Mathematical Sciences》1996,106(3):301-328
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 invarian theory. 相似文献
9.
Matei Toma 《Central European Journal of Mathematics》2012,10(4):1356-1360
We show that certain moduli spaces of vector bundles over blown-up primary Hopf surfaces admit no compact components. These
are the moduli spaces used by Andrei Teleman in his work on the classification of class VII surfaces. 相似文献
10.
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
11.
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
12.
13.
Thomas Nevins 《Transformation Groups》2009,14(4):931-983
We give a generic spectral decomposition of the derived category of twisted D\mathcal{D} -modules on a moduli stack of mirabolic vector bundles on a curve X in characteristic p: that is, we construct an equivalence with the derived category of quasicoherent sheaves on a moduli stack of mirabolic local
systems on X. This equivalence may be understood as a tamely ramified form of the geometric Langlands equivalence. When X has genus 1, this equivalence generically solves (in the sense of noncommutative geometry) the quantum Calogero–Moser system. 相似文献
14.
Luis álvarez-Cónsul 《Geometriae Dedicata》2009,139(1):99-120
This article is concerned with the study of gauge theory, stability and moduli for twisted quiver bundles in algebraic geometry.
We review natural vortex equations for twisted quiver bundles and their link with a stability condition. Then we provide a
brief overview of their relevance to other geometric problems and explain how quiver bundles can be viewed as sheaves of modules
over a sheaf of associative algebras and why this view point is useful, e.g., in their deformation theory. Next we explain
the main steps of an algebro-geometric construction of their moduli spaces. Finally, we focus on the special case of holomorphic
chains over Riemann surfaces, providing some basic links with quiver representation theory. Combined with the analysis of
the homological algebra of quiver sheaves and modules, these links provide a criterion for smoothness of the moduli spaces
and tools to study their variation with respect to stability.
相似文献
15.
Tarig Abdelgadir 《代数通讯》2013,41(2):636-649
We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their canonical bundles, and show that they are rarely tilting. We also give a moduli construction for these total spaces for weighted projective lines with three orbifold points. 相似文献
16.
17.
Over a smooth complex projective curve of genus ≥3, we study 1-cycles on the moduli space of rank-2 stable vector bundles with fixed determinant of degree 1. We show the first Chow group of the moduli space is isomorphic to the zeroth Chow group of the curve. 相似文献
18.
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
19.
Maslov complex germs (complex vector bundles, satisfying certain additional conditions, over isotropic submanifolds of the phase space) are one of the central objects in the theory of semiclassical quantization. To these bundles one assigns spectral series (quasimodes) of partial differential operators. We describe the moduli spaces of Maslov complex germs over a point and a closed trajectory and find the moduli of complex germs generated by a given symplectic connection over an invariant torus. 相似文献
20.
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.