Moduli spaces of toric manifolds

被引：10

作者：

Pelayo, A. ^{[1
,2
]}

Pires, A. R. ^{[3
]}

Ratiu, T. S. ^{[4
,5
]}

Sabatini, S. ^{[4
]}

机构：

[1] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA

[2] Washington Univ, Dept Math, St Louis, MO 63130 USA

[3] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

[4] Ecole Polytech Fed Lausanne, Sect Math, Stn 8, CH-1015 Lausanne, Switzerland

[5] Ecole Polytech Fed Lausanne, Bernoulli Ctr, Stn 8, CH-1015 Lausanne, Switzerland

来源：

GEOMETRIAE DEDICATA | 2014年 / 169卷 / 01期

关键词：

Toric manifold; Delzant polytope; Moduli space; Metric space; CONVEXITY;

D O I：

10.1007/s10711-013-9858-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction of the distance is related to the Duistermaat-Heckman measure and the Hausdorff metric. While the moduli space, its topology and metric, may be constructed in any dimension, the tools we use in the proofs are four-dimensional, and hence so is our main result.

引用

页码：323 / 341

页数：19

共 50 条

[31] Hyperbolicity of Moduli Spaces of Log-Canonically Polarized Manifolds
Wing-Keung To
Sai-Kee Yeung
The Journal of Geometric Analysis, 2021, 31 : 2941 - 2969
[32] Weil-Petersson volumes of the moduli spaces of CY manifolds
Todorov, Andrey
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2007, 15 (02) : 407 - 434
[33] Hyperbolicity of Moduli Spaces of Log-Canonically Polarized Manifolds
To, Wing-Keung
Yeung, Sai-Kee
JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (03) : 2941 - 2969
[34] Orbit configuration spaces of small covers and quasi-toric manifolds
Junda Chen
Zhi Lü
Jie Wu
Science China Mathematics, 2021, 64 : 167 - 196
[35] MODULI SPACES OF ORIENTED TYPE A MANIFOLDS OF DIMENSION AT LEAST 3
Gilkey, Peter
Park, JeongHyeong
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2017, 54 (06) : 1759 - 1786
[36] TAUTOLOGICAL CLASSES ON MODULI SPACES OF HYPER-KAHLER MANIFOLDS
Bergeron, Nicolas
Li, Zhiyuan
DUKE MATHEMATICAL JOURNAL, 2019, 168 (07) : 1179 - 1230
[37] Orbit configuration spaces of small covers and quasi-toric manifolds
Junda Chen
Zhi Lü
Jie Wu
Science China(Mathematics), 2021, 64 (01) : 167 - 196
[38] Poincar, polynomials of moduli spaces of stable maps into flag manifolds
Zhuang, Xiaobo
FRONTIERS OF MATHEMATICS IN CHINA, 2018, 13 (02) : 483 - 508
[39] Poincaré polynomials of moduli spaces of stable maps into flag manifolds
Xiaobo Zhuang
Frontiers of Mathematics in China, 2018, 13 : 483 - 508
[40] QUOTIENTS OF COMPLEX-MANIFOLDS AND MODULI SPACES OF KLEIN SURFACES
SEPPALA, M
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 1981, 6 (01): : 113 - 124

← 1 2 3 4 5 →