共查询到20条相似文献,搜索用时 31 毫秒
1.
We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo–Mumford regularity of such sheaves, which we provide. 相似文献
2.
Fourier-Mukai transforms for coherent systems on elliptic curves 总被引:1,自引:0,他引:1
Ruiperez Daniel Hernandez; Prieto Carlos Tejero 《Journal London Mathematical Society》2008,77(1):15-32
We determine all the Fourier–Mukai transforms for coherentsystems consisting of a vector bundle over an elliptic curveand a subspace of its global sections, showing that these transformsare indexed by positive integers. We prove that the naturalstability condition for coherent systems, which depends on aparameter, is preserved by these transforms for small and largevalues of the parameter. By means of the Fourier–Mukaitransforms we prove that certain moduli spaces of coherent systemscorresponding to small and large values of the parameter areisomorphic. Using these results we draw some conclusions aboutthe possible birational type of the moduli spaces. We provethat for a given degree d of the vector bundle and a given dimensionof the subspace of its global sections there are at most d differentpossible birational types for the moduli spaces. 相似文献
3.
We formulate three versions of a strange duality conjecture for sections of the Theta bundles on the moduli spaces of sheaves on abelian surfaces. As supporting evidence, we check the equality of dimensions on dual moduli spaces, answering a question raised by Göttsche et al. (K-theoretic Donaldson invariants via instanton counting. arXiv:math/0611945). 相似文献
4.
Gülay Karadoğan-Kaya 《Archiv der Mathematik》2007,89(4):315-325
In this paper, we study the structure, deformations and the moduli spaces of complex projective surfaces admitting genus two
fibrations over elliptic curves. We observe that a surface admitting a smooth fibration as above is elliptic, and we employ
results on the moduli of polarized elliptic surfaces to construct moduli spaces of these smooth fibrations. In the case of
nonsmooth fibrations, we relate the moduli spaces to the Hurwitz schemes
of morphisms of degree n from elliptic curves to the modular curve X(d), d ≥ 3. Ultimately, we show that the moduli spaces in the nonsmooth case are fiber spaces over the affine line
with fibers determined by the components of
.
Received: 30 August 2006 相似文献
5.
Brendan Hassett 《Advances in Mathematics》2003,173(2):316-352
A weighted pointed curve consists of a nodal curve and a sequence of marked smooth points, each assigned a number between zero and one. A subset of the marked points may coincide if the sum of the corresponding weights is no greater than one. We construct moduli spaces for these objects using methods of the log minimal model program, and describe the induced birational morphisms between moduli spaces as the weights are varied. In the genus zero case, we explain the connection to Geometric Invariant Theory quotients of points in the projective line, and to compactifications of moduli spaces studied by Kapranov, Keel, and Losev-Manin. 相似文献
6.
In this paper we construct certain moduli spaces, which we call
moduli spaces of (principal) F-bundles,
and study their basic properties. These spaces are
associated to triples consisting of a smooth projective geometrically
connected curve over a finite field, a split
reductive group G, and an irreducible
algebraic representation
.of
of
Our spaces generalize moduli
spaces of F-sheaves, studied
by Drinfeld and Lafforgue, which correspond to the case G
= GLr
and
is the tensor product of the standard
representation and its dual. The importance of the moduli spaces
of F-bundles is due to the
belief that Langlands correspondence is realized in their cohomology. 相似文献
7.
We construct new “virtually smooth” modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties. They generalize Givental's compactifications, when the complex structure of the curve is allowed to vary and markings are included, and are the toric counterpart of the moduli spaces of stable quotients introduced by Marian, Oprea, and Pandharipande to compactify spaces of maps to Grassmannians. A brief discussion of the resulting invariants and their (conjectural) relation with Gromov-Witten theory is also included. 相似文献
8.
9.
This article is a survey of basic facts about the moduli spaces of stable surfaces. These spaces are projective compactifications of the moduli spaces of minimal surfaces of general type. They share few of the nice features of the moduli spaces of stable curves. Some of the main pathologies are presented with some historical remarks and some more recent results on the boundary of these spaces.Received: February, 2004 相似文献
10.
Kōta Yoshioka 《Mathematische Annalen》2001,321(4):817-884
In this paper, we consider basic problems on moduli spaces of stable sheaves on abelian surfaces. Our main assumption is
the primitivity of the associated Mukai vector. We determine the deformation types, albanese maps, Bogomolov factors and their
weight 2 Hodge structures. We also discuss the deformation types of moduli spaces of stable sheaves on K3 surfaces.
Received: 28 February 2000 / Revised version: 15 September 2000 / Published online: 24 September 2001 相似文献
11.
Michael A. van Opstall 《Archiv der Mathematik》2005,84(2):148-154
Some technical results on the deformations of varieties of general type and on permanence of semi-log-canonical singularities are proved. These results are applied to show that the connected component of the moduli space of stable surfaces containing the moduli point of a product of stable curves is the product of the moduli spaces of the curves, assuming the curves have different genera. An application of this result shows that even after compactifying the moduli space and fixing numerical invariants, the moduli spaces are still very disconnected.Received: 20 February 2004 相似文献
12.
Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic;
the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When
S have holes, we defined two moduli spaces closely related to the moduli spaces of G-local systems on S. We show that they
carry a lot of interesting structures. In particular we define a distinguished collection of coordinate systems, equivariant
under the action of the mapping class group of S. We prove that their transition functions are subtraction free. Thus we have
positive structures on these moduli spaces. Therefore we can take their points with values in any positive semifield. Their
positive real points provide the two higher Teichmüller spaces related to G and S, while the points with values in the tropical
semifields provide the lamination spaces. We define the motivic avatar of the Weil–Petersson form for one of these spaces.
It is related to the motivic dilogarithm. 相似文献
13.
We prove that the Fano variety of lines of a generic cubic fourfold containing a plane is isomorphic to a moduli space of twisted stable complexes on a K3 surface. On the other hand, we show that the Fano varieties are always birational to moduli spaces of twisted stable coherent sheaves on a K3 surface. The moduli spaces of complexes and of sheaves are related by wall-crossing in the derived category of twisted sheaves on the corresponding K3 surface. 相似文献
14.
Thorsten Weist 《Journal of Pure and Applied Algebra》2011,215(10):2406-2422
By a result of Klyachko the Euler characteristic of moduli spaces of stable bundles of rank two on the projective plane is determined. Using similar methods we extend this result to bundles of rank three. The fixed point components correspond to moduli spaces of the subspace quiver. Moreover, the stability condition is given by a certain system of linear inequalities so that the generating function of the Euler characteristic can be determined explicitly. 相似文献
15.
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
16.
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
17.
We study the coherent orientations of the moduli spaces of holomorphic curves in Symplectic Field Theory, generalizing a construction due to Floer and Hofer. In particular we examine their behavior at multiple closed Reeb orbits under change of the asymptotic direction. The orientations are determined by a certain choice of orientation at each closed Reeb orbit, that is similar to the orientation of the unstable tangent spaces of critical points in finite–dimensional Morse theory.in final form: 22 October 2003 相似文献
18.
Dmitry N. Kozlov 《Topology and its Applications》2008,156(2):433-437
In this paper we study homotopy type of certain moduli spaces of metric graphs. More precisely, we show that the spaces , which parametrize the isometry classes of metric graphs of genus 1 with n marks on vertices are homotopy equivalent to the spaces TM1,n, which are the moduli spaces of tropical curves of genus 1 with n marked points. Our proof proceeds by providing a sequence of explicit homotopies, with key role played by the so-called scanning homotopy. We conjecture that our result generalizes to the case of arbitrary genus. 相似文献
19.
We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kähler manifold X. These solutions are known to be related to polystable triples via a Kobayashi–Hitchin type correspondence. Using a characterization of infinitesimal deformations in terms of the cohomology of a certain elliptic double complex, we construct a Hermitian structure on these moduli spaces. This Hermitian structure is proved to be Kähler. The proof involves establishing a fiber integral formula for the Hermitian form. We compute the curvature tensor of this Kähler form. When X is a Riemann surface, the holomorphic bisectional curvature turns out to be semi-positive. It is shown that in the case where X is a smooth complex projective variety, the Kähler form is the Chern form of a Quillen metric on a certain determinant line bundle. 相似文献
20.
Peter Vermeire 《Journal of Pure and Applied Algebra》2007,211(3):622-632
We compute the expected dimension of the moduli space of torsion-free rank 2 sheaves at a point corresponding to a stable reflexive sheaf, and give conditions for the existence of a perfect tangent-obstruction complex on a class of smooth projective threefolds; this class includes Fano and Calabi-Yau threefolds. We also explore both local and global relationships between moduli spaces of reflexive rank 2 sheaves and the Hilbert scheme of curves. 相似文献