On the Kahler metrics over Symd (X)

被引：5

作者：

Aryasomayajula, Anilatmaja ^{[1
]}

Biswas, Indranil ^{[2
]}

Morye, Archana S. ^{[1
]}

Sengupta, Tathagata ^{[1
]}

机构：

[1] Univ Hyderabad, Dept Math, Prof CR Rao Rd, Hyderabad 500046, Andhra Pradesh, India

[2] Tata Inst Fundamental Res, Sch Math, Homi Bhabha Rd, Bombay 400005, Maharashtra, India

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2016年 / 110卷

关键词：

Symmetric product; Jacobian; Bergman kernel; Petersson inner product; VORTEX MODULI SPACES; VORTICES; EQUATIONS; BUNDLES;

D O I：

10.1016/j.geomphys.2016.08.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

LetX be a compact connected Riemann surface of genus g, with g >= 2. For each d < eta(x), where eta(X) is the gonality of X, the symmetric product Sym(d)(X) embeds into Pic(d)(X) by sending an effective divisor of degree d to the corresponding holomorphic line bundle. Therefore, the restriction of the flat Kahler metric on Picd (X) is a Rattler metric on Sym(d) (X). We investigate this Kahler metric on Sym(d)(X). In particular, we estimate it is Bergman kernel. We also prove that any holomorphic automorphism of Sym(d) (X) is an isometry. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：187 / 194

页数：8

共 16 条

[1] On the L2-metric of vortex moduli spaces
Baptista, J. M.
[J]. NUCLEAR PHYSICS B, 2011, 844 (02) : 308 - 333
[2] VORTICES IN HOLOMORPHIC LINE BUNDLES OVER CLOSED KAHLER-MANIFOLDS
BRADLOW, SB
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 135 (01) : 1 - 17
[3] BRADLOW SB, 1991, J DIFFER GEOM, V33, P169
[4] Chen B.-Y., 2016, J DIFFERENTIAL GEOM
[5] Fakhruddin N., ARXIV0208180V1
[6] Friedman J.S., ARXIV13051348
[7] A DIRECT EXISTENCE PROOF FOR THE VORTEX EQUATIONS OVER A COMPACT RIEMANN SURFACE
GARCIAPRADA, O
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1994, 26 : 88 - 96
[8] Bounds on canonical Green's functions
Jorgenson, J
Kramer, J
[J]. COMPOSITIO MATHEMATICA, 2006, 142 (03) : 679 - 700
[9] Jorgenson J., 1995, QUAEST MATH, V18, P345
[10] MACDONALD I. G., 1962, Topology, V1, P319, DOI [10.1016/0040-9383(62)90019-8, DOI 10.1016/0040-9383(62)90019-8]

← 1 2 →