On boundedness and moduli spaces of K-stable Calabi-Yau fibrations over curves

被引：1
作者：
Hashizume, Kenta [1 ]
Hattori, Masafumi [2 ]
机构：
[1] Niigata Univ, Fac Sci, Dept Math, Niigata, Japan
[2] Kyoto Univ, Grad Sch Sci, Dept Math, Kyoto, Japan
来源：
GEOMETRY & TOPOLOGY | 2025年 / 29卷 / 03期
关键词：
CURVATURE KAHLER-METRICS; SCALAR CURVATURE; EINSTEIN METRICS; FANO VARIETIES; GLOBAL MODULI; STABILITY; SINGULARITIES; THEOREMS; MANIFOLDS; EXISTENCE;
D O I：
10.2140/gt.2025.29.1619
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show boundedness of polarized Calabi-Yau fibrations over curves only with fixed volumes of general fibers and Iitaka volumes. As its application, we construct a separated coarse moduli space of K-stable Calabi-Yau fibrations over curves in an adiabatic sense (Hattori 2022) and show that all members (resp. smooth members) of the moduli are simultaneously uniformly K-stable (resp. have cscK metrics) for a certain choice of polarizations.
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页码：1619 / 1691
页数：76
相关论文
共 92 条
[1]  
Alexeev V, 1996, HIGHER DIMENSIONAL COMPLEX VARIETIES, P1
[2]  
Alexeev V, 1996, arXiv
[3]   Reductivity of the automorphism group of K-polystable Fano varieties [J].
Alper, Jarod ;
Blum, Harold ;
Halpern-Leistner, Daniel ;
Xu, Chenyang .
INVENTIONES MATHEMATICAE, 2020, 222 (03) :995-1032
[4]  
Ambro F, 2004, J DIFFER GEOM, V67, P229, DOI 10.4310/jdg/1102536201
[5]  
Belmans P, 2005, The Stacks project, electronic reference
[6]  
Birkar C.:., 2019, ANN MATH, V190, P345, DOI DOI 10.4007/annals.2019.190.2.1
[7]  
Birkar C., Moduli of algebraic varieties
[8]   Geometry of polarised varieties [J].
Birkar, Caucher .
PUBLICATIONS MATHEMATIQUES DE L IHES, 2023, 137 (01) :47-105
[9]  
Birkar C, 2021, Arxiv, DOI arXiv:2103.14935
[10]   Singularities of linear systems and boundedness of Fano varieties [J].
Birkar, Caucher .
ANNALS OF MATHEMATICS, 2021, 193 (02) :347-405
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