Boundedness of the space of stable logarithmic maps

被引：29

作者：

Abramovich, Dan ^{[1
]}

Chen, Qile ^{[2
]}

Marcus, Steffen ^{[3
]}

Wise, Jonathan ^{[4
]}

机构：

[1] Brown Univ, Dept Math, Box 1917, Providence, RI 02912 USA

[2] Boston Coll, Dept Math, 140 Commonwealth Ave, Chestnut Hill, MA 02467 USA

[3] Coll New Jersey, Dept Math & Stat, Ewing, NJ 08628 USA

[4] Univ Colorado, Dept Math, Boulder, CO 80309 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2017年 / 19卷 / 09期

基金：

美国国家科学基金会;

关键词：

Stable maps; logarithmic structures; moduli spaces; algebraic stacks; GROMOV-WITTEN INVARIANTS; FACTORIZATION THEOREM; PAIRS; SCHEMES; CURVES; MODULI; TROPICALIZATION; DEGENERATIONS; GEOMETRY;

D O I：

10.4171/JEMS/728

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the moduli space of stable logarithmic maps with fixed numerical invariants, from logarithmic curves to a fixed projective target logarithmic scheme with fine and saturated logarithmic structure, is a proper algebraic stack. This was previously known only with further restrictions on the logarithmic structure of the target.

引用

页码：2783 / 2809

页数：27

共 33 条

[1] A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension [J].

Abramovich, D ;

Matsuki, K ;

Rashid, S .

TOHOKU MATHEMATICAL JOURNAL, 1999, 51 (04) :489-537

[2] Weak semistable reduction in characteristic 0 [J].

Abramovich, D ;

Karu, K .

INVENTIONES MATHEMATICAE, 2000, 139 (02) :241-273

[3]

ABRAMOVICH D., 2016, Nonarchimedean and Tropical Geometry, P287

[4]

Abramovich D., 2013, UNPUB

[5]

Abramovich D., 2013, Adv. Lect. Math. (ALM), V24, P1

[6]

Abramovich D., 2010, ARXIV10040981

[7]

Abramovich D, 2015, ANN SCI ECOLE NORM S, V48, P765

[8] COMPARISON THEOREMS FOR GROMOV-WITTEN INVARIANTS OF SMOOTH PAIRS AND OF DEGENERATIONS [J].

Abramovich, Dan ;

Marcus, Steffen ;

Wise, Jonathan .

ANNALES DE L INSTITUT FOURIER, 2014, 64 (04) :1611-1667

[9] STABLE LOGARITHMIC MAPS TO DELIGNE-FALTINGS PAIRS II [J].

Abramovich, Dan ;

Chen, Qile .

ASIAN JOURNAL OF MATHEMATICS, 2014, 18 (03) :465-488

[10] Expanded Degenerations and Pairs [J].

Abramovich, Dan ;

Cadman, Charles ;

Fantechi, Barbara ;

Wise, Jonathan .

COMMUNICATIONS IN ALGEBRA, 2013, 41 (06) :2346-2386

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