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1.
An approach to a natural geometry of moduli spaces of symplectic structures is presented.
Received: 21 March 2002 / Revised version: 28 August 2002
This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG). 相似文献
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We determine the necessary and sufficient conditions for the based SU(l)-instanton moduli spaces over CP2 and the unbased SU(2)-instanton moduli spaces over S4 having spin structures. 相似文献
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Bohui Chen 《数学学报(英文版)》2010,26(2):209-240
The bubble tree compactified instanton moduli space -Mκ (X) is introduced. Its singularity set Singκ(X) is described. By the standard gluing theory, one can show that- Mκ(X) - Singκ(X) is a topological orbifold. In this paper, we give an argument to construct smooth structures on it. 相似文献
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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
6.
《代数通讯》2013,41(10):4871-4897
Abstract In order to study the Hochschild cohomology of an n-triangular algebra 𝒯 n , we construct a spectral sequence, whose terms are parametrized by the length of the trajectories of the quiver associated with 𝒯 n , and which converges to the Hochschild cohomology of 𝒯 n . We describe explicitly its components and its differentials which are sums of cup products. In case n = 3 we study some properties of the differential at level 2. We give some examples of use of the spectral sequence and recover formulas for the dimension of the cohomology groups of particular cases of triangular algebras. 相似文献
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In this paper we prove that the moduli spaces MI
2n+1(k) of mathematical instanton bundles on 2n+1
with quantum number k are singular for n 2 and k 3 ,giving a positive answer to a conjecture made by Ancona and Ottaviani in 1993. 相似文献
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The aim of this paper is to investigate the first Hochschild
cohomology of admissible algebras which can be regarded as a
generalization of basic algebras. For this purpose, the authors
study differential operators on an admissible algebra. Firstly,
differential operators from a path algebra to its quotient algebra
as an admissible algebra are discussed. Based on this discussion,
the first cohomology with admissible algebras as coefficient modules
is characterized, including their dimension formula. Besides, for
planar quivers, the $k$-linear bases of the first cohomology of
acyclic complete monomial algebras and acyclic truncated quiver
algebras are constructed over the field $k$ of characteristic $0$. 相似文献
10.
Georg Schumacher 《manuscripta mathematica》1985,50(1):229-267
We construct a Kähler metric on the moduli spaces of compact complex manifolds with c1,<0 and of polarized compact Kähler manifolds with c1=0, which is a generalization of the Petersson-Well metric. It is induced by the variation of the Kähler-Einstein metrics on the fibers that exist according to the Calabi-Yau theorem. We compute the above metric on the moduli spaces of polarized tori and symplectic manifolds. It turns out to be the Maaß metric on the Siegel upper half space and the Bergmann metric on a symmetric space of type III resp. In particular it is Kähler-Einstein with negative curvature.Dedicated to Karl SteinHeisenberg-Stipendiat der Deutschen Forschungsgemeinschaft 相似文献
11.
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
12.
Paolo Lisca 《Transactions of the American Mathematical Society》2008,360(2):765-799
Let be the contact structure naturally induced on the lens space by the standard contact structure on the three-sphere . We obtain a complete classification of the symplectic fillings of up to orientation-preserving diffeomorphisms. In view of our results, we formulate a conjecture on the diffeomorphism types of the smoothings of complex two-dimensional cyclic quotient singularities.
13.
We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of the moduli spaces (which are symmetric products of the surface), we prove that, for genus $g>1$ , the holomorphic bisectional curvature of the vortex metrics cannot always be nonnegative in the multivortex case, and this property extends to all Kähler metrics on certain symmetric products. Our result rules out an established and natural conjecture on the geometry of the moduli spaces. 相似文献
14.
Lucio Guerra 《Annali di Matematica Pura ed Applicata》2006,185(3):319-335
We describe the moduli spaces of morphisms between polarized complex abelian varieties. The discrete invariants, derived from
a Poincaré decomposition of morphisms, are the types of polarizations and of lattice homomorphisms occurring in the decomposition.
For a given type of morphisms the moduli variety is irreducible, and is obtained from a product of Siegel spaces modulo the
action of a discrete group.
Mathematics Subject Classification (2000) 14K20 相似文献
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Kim A. Frøyshov 《Topology》2004,43(2):407-432
Given a smooth, compact, oriented 4-manifold X with a homology sphere Y as boundary and b2+(X)=1, and given an embedded surface Σ⊂X of self-intersection 1, we prove an inequality relating h(Y), the genus of Σ, and a certain invariant of the orthogonal complement of [Σ] in the intersection form of X. 相似文献
18.
Inspired by recent work of Cerulli, Feigin and Reineke on desingularizations of quiver Grassmannians of representations of Dynkin quivers, we obtain desingularizations in considerably more general situations and in particular for Grassmannians of modules over iterated tilted algebras of Dynkin type. Our desingularization map is constructed from Nakajima's desingularization map for graded quiver varieties. 相似文献
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Thorsten Weist 《Journal of Algebraic Combinatorics》2013,38(3):567-583
Combining the MPS degeneration formula for the Poincaré polynomial of moduli spaces of stable quiver representations and localization theory, it turns that the determination of the Euler characteristic of these moduli spaces reduces to a combinatorial problem of counting certain trees. We use this fact in order to obtain an upper bound for the Euler characteristic in the case of the Kronecker quiver. We also derive a formula for the Euler characteristic of some of the moduli spaces appearing in the MPS degeneration formula. 相似文献