Mumford's influence on the moduli theory of algebraic varieties

被引：0

作者：

Kollar, Janos ^{[1
]}

机构：

[1] Princeton Univ, Princeton, NJ 08544 USA

来源：

PURE AND APPLIED MATHEMATICS QUARTERLY | 2021年 / 17卷 / 02期

关键词：

LOG; BOUNDEDNESS; ADJUNCTION; STABILITY; SURFACES; GEOMETRY;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a short appreciation of Mumford's work on the moduli of varieties by putting it into historical context. By reviewing earlier works we highlight the innovations introduced by Mumford. Then we discuss recent developments whose origins can be traced back to Mumford's ideas.

引用

页码：619 / 647

页数：29

共 50 条

[31] Some result in the arithmetic theory of algebraic varieties
Zariski, O
AMERICAN JOURNAL OF MATHEMATICS, 1939, 61 : 249 - 294
[32] ON THE HOMOLOGY THEORY OF ALGEBRAIC VARIETIES .1.
WALLACE, AH
ANNALS OF MATHEMATICS, 1956, 63 (02) : 248 - 271
[33] Algebraic BP-theory and norm varieties
Yagita, Nobuaki
HOKKAIDO MATHEMATICAL JOURNAL, 2012, 41 (02) : 275 - 316
[34] MODULI SPACES FOR REAL ALGEBRAIC-CURVES AND REAL ABELIAN-VARIETIES
SEPPALA, M
SILHOL, R
MATHEMATISCHE ZEITSCHRIFT, 1989, 201 (02) : 151 - 165
[35] Abelian varieties of the Mumford type
Galluzzi, F
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2000, 3A : 81 - 84
[36] On algebraic K-theory of real algebraic varieties with circle action
Ozan, Y
JOURNAL OF PURE AND APPLIED ALGEBRA, 2002, 170 (2-3) : 287 - 293
[37] New and old results on spherical varieties via moduli theory
Avdeev, Roman
Cupit-Foutou, Stephanie
ADVANCES IN MATHEMATICS, 2018, 328 : 1299 - 1352
[38] Recursion Between Mumford Volumes of Moduli Spaces
Eynard, Bertrand
ANNALES HENRI POINCARE, 2011, 12 (08): : 1431 - 1447
[39] INTERSECTION THEORY ON ALGEBRAIC STACKS AND Q-VARIETIES
GILLET, H
JOURNAL OF PURE AND APPLIED ALGEBRA, 1984, 34 (2-3) : 193 - 240
[40] Towards an intersection homology theory for real algebraic varieties
van Hamel, J
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2003, 2003 (25) : 1395 - 1411

← 1 2 3 4 5 →