共查询到20条相似文献,搜索用时 812 毫秒
1.
We show that surface bundles over surfaces with base and fiber of genus at least have non-vanishing simplicial volume.
2.
The existence problem for holomorphic structures on vector bundles over non-algebraic surfaces is, in general, still open. We solve this problem in the case of rank 2 vector bundles over K3 surfaces and in the case of vector bundles of arbitrary rank over all known surfaces of class VII. Our methods, which are based on Donaldson theory and deformation theory, can be used to solve the existence problem of holomorphic vector bundles on further classes of non-algebraic surfaces. To cite this article: A. Teleman, M. Toma, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 383–388. 相似文献
3.
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
4.
5.
Marco Matone 《Transactions of the American Mathematical Society》2004,356(8):2989-3004
We find an infinite set of eigenfunctions for the Laplacian with respect to a flat metric with conical singularities and acting on degree zero bundles over special Riemann surfaces of genus greater than one. These special surfaces correspond to Riemann period matrices satisfying a set of equations which lead to a number theoretical problem. It turns out that these surfaces precisely correspond to branched covering of the torus. This reflects in a Jacobian with a particular kind of complex multiplication.
6.
7.
Tomokuni Takahashi 《Mathematische Nachrichten》2013,286(4):402-429
We classify the algebraic surfaces with Eisenbud‐Harris general fibration of genus 4 over a rational curve or an elliptic curve whose slope attains the lower bound. The classification of our surfaces is strongly related to the result of the classification for certain relative quadric hypersurfaces in 3‐dimensional projective space bundles over a rational curve and an elliptic curve. We further prove some results about the canonical maps, the quadric hulls of the canonical images and the deformation for these surfaces. 相似文献
8.
We describe a circle-sum construction of smoothly embedded surface in a smooth 4-manifold. We apply this construction to give a simpler solution of the minimal genus problem for nontrivial bundles over surfaces. We also treat the case of blow-ups.
9.
Brian H. Bowditch 《Geometric And Functional Analysis》2009,19(4):943-988
A surface-by-surface group is an extension of a non-trivial orientable closed surface group by another such group. It is an
open question as to whether every such group contains a free abelian subgroup of rank 2. We show that, for given base and
fibre genera, all but finitely many isomorphism classes of surface-by-surface group contain such an abelian subgroup. This
can be rephrased in terms of atoroidal surface bundles over surfaces, or in terms of purely loxodromic surface subgroups of
the mapping class groups. 相似文献
10.
V. Balaji 《Proceedings Mathematical Sciences》1995,105(4):371-380
For smooth projective varietiesX over ℂ, the Hodge Conjecture states that every rational Cohomology class of type (p, p) comes from an algebraic cycle. In this paper, we prove the Hodge conjecture for some moduli spaces of vector bundles on
compact Riemann surfaces of genus 2 and 3. 相似文献
11.
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
12.
Thierry Lévy 《Probability Theory and Related Fields》2006,136(2):171-202
In this paper, we construct one Yang-Mills measure on an orientable compact surface for each isomorphism class of principal
bundles with compact connected structure group over this surface. For this, we refine the discretization procedure used in
a previous construction [9] and define a discrete theory on a new configuration space which is essentially a covering of the
usual one. We prove that the measures corresponding to different isomorphism classes of bundles or to different total areas
of the base space are mutually singular. We give also a combinatorial computation of the partition functions which relies
on the formalism of fat graphs. 相似文献
13.
The aim of the paper is to give an explicit expression for Hitchin's connection in the case of stable rank 2 bundles on genus 2 curves. Some general theory (in the algebraic geometric setting) concerning heat operators is developed. In particular the notion of compatibility of a heat operator with respect to a closed subvariety is introduced. This is used to compare the heat operator in the nonabelian rank 2 genus 2 case to the abelian heat operator (on theta functions) for abelian surfaces. This relation allows one to perform the computation; the resulting differential equations are similar to the Knizhnik-Zalmolodshikov equations.
14.
Harmonic and analytic functions have natural discrete
analogues. Harmonic functions can be defined on every graph, while
analytic functions (or, more precisely, holomorphic forms) can be
defined on graphs embedded in orientable surfaces. Many important
properties of the "true" harmonic and analytic functions can be
carried over to the discrete setting. We prove that a nonzero analytic
function can vanish only on a very small connected piece. As an
application, we describe a simple local random process on embedded
graphs, which have the property that observing them in a small
neighborhood of a node through a polynomial time, we can infer the genus
of the surface. 相似文献
15.
Viktoria Heu 《Mathematische Annalen》2009,344(2):463-490
We are interested in the stability of holomorphic rank 2 vector bundles of degree 0 over compact Riemann surfaces, which are
provided with irreducible meromophic tracefree connections. In the case of a logarithmic connection on the Riemann sphere,
such a vector bundle will be trivial up to the isomonodromic deformation associated to a small move of the poles, according
to a result of A. Bolibruch. In the general case of meromorphic connections over Riemann surfaces of arbitrary genus, we prove
that the vector bundle will be semi-stable, up to a small isomonodromic deformation. More precisely, the vector bundle underlying
the universal isomonodromic deformation is generically semi-stable along the deformation, and even maximally stable. For curves
of genus g ≥ 2, this result is non-trivial even in the case of non-singular connections.
The author was partially supported by ANR SYMPLEXE BLAN06-3-137237. 相似文献
16.
The presentation of the quantum cohomology of the moduli spaceof stable vector bundles of rank two and odd degree with fixeddeterminant over a Riemann surface of genus g > 2 is obtained.The argument avoids the use of gauge theory, providing an alternativeproof to that given by the author in Duke Math. J. 98 (1999)525540. 2000 Mathematics Subject Classification 14N35(primary); 14H60, 53D45 (secondary). 相似文献
17.
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
18.
Lin Weng 《Mathematische Annalen》2001,320(2):239-283
In Part I, Deligne-Riemann-Roch isometry is generalized for punctured Riemann surfaces equipped with quasi-hyperbolic metrics.
This is achieved by proving the Mean Value Lemmas, which explicitly explain how metrized Deligne pairings for -admissible metrized line bundles depend on . In Part II, we first introduce several line bundles over Knudsen-Deligne-Mumford compactification of the moduli space (or
rather the algebraic stack) of stable N-pointed algebraic curves of genus g, which are rather natural and include Weil-Petersson, Takhtajan-Zograf and logarithmic Mumford line bundles. Then we use
Deligne-Riemann-Roch isomorphism and its metrized version (proved in Part I) to establish some fundamental relations among
these line bundles. Finally, we compute first Chern forms of the metrized Weil-Petersson, Takhtajan-Zograf and logarithmic
Mumford line bundles by using results of Wolpert and Takhtajan-Zograf, and show that the so-called Takhtajan-Zograf metric
on the moduli space is algebraic.
Received February 14, 2000 / Accepted August 18, 2000 / Published online February 5, 2001 相似文献
19.
Mitsuru Kawazoe 《Journal of Pure and Applied Algebra》2006,204(3):602-615
Elliptic surfaces over an algebraically closed field in characteristic p>0 with multiple supersingular elliptic fibers, that is, multiple fibers of a supersingular elliptic curve, are investigated. In particular, it is shown that for an elliptic surface with q=g+1 and a supersingular elliptic curve as a general fiber, where q is the dimension of an Albanese variety of the surface and g is the genus of the base curve, the multiplicities of the multiple supersingular elliptic fibers are not divisible by p2. As an application of this result, the structure of false hyperelliptic surfaces is discussed on this basis. 相似文献
20.
Justin Sawon 《Geometriae Dedicata》2014,171(1):93-117
Four-folds with trivial canonical bundles are divided into six classes according to their holonomy group. We consider examples that are fibred by abelian surfaces over the projective plane. We construct such fibrations in five of the six classes, and prove that there is no such fibration in the sixth class. We classify all such fibrations whose generic fibre is the Jacobian of a genus two curve. 相似文献