Relative and orbifold Gromov-Witten invariants

被引：12

作者：

Abramovich, Dan ^{[1
]}

Cadman, Charles ^{[2
]}

Wise, Jonathan ^{[3
]}

机构：

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

[2] Munich Re, Suite 500,56 Perimeter Ctr East, Atlanta, GA 30346 USA

[3] Univ Colorado, Campus Box 395, Boulder, CO 80309 USA

来源：

ALGEBRAIC GEOMETRY | 2017年 / 4卷 / 04期

关键词：

Gromov-Witten invariants; virtual fundamental class; orbifold curves; STABLE LOGARITHMIC MAPS; PAIRS; FORMULA; STACKS; DEGENERATIONS; CURVES;

D O I：

10.14231/AG-2017-025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that genus 0 Gromov-Witten invariants of a smooth scheme relative to a smooth divisor coincide with genus 0 orbifold Gromov-Witten invariants of an appropriate root stack construction along the divisor. The proof is given at the level of virtual fundamental classes.

引用

页码：472 / 500

页数：29

共 26 条

[1] Compactifying the space of stable maps [J].

Abramovich, D ;

Vistoli, A .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 15 (01) :27-75

[2]

Abramovich D, 2008, AM J MATH, V130, P1337

[3] Configurations of points on degenerate varieties and properness of moduli spaces [J].

Abramovich, Dan ;

Fantechi, Barbara .

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2017, 137 :1-17

[4]

Abramovich D, 2016, ANN SCUOLA NORM-SCI, V16, P519

[5] 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

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

Abramovich, Dan ;

Chen, Qile .

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

[7] Expanded Degenerations and Pairs [J].

Abramovich, Dan ;

Cadman, Charles ;

Fantechi, Barbara ;

Wise, Jonathan .

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

[8] The intrinsic normal cone [J].

Behrend, K ;

Fantechi, B .

INVENTIONES MATHEMATICAE, 1997, 128 (01) :45-88

[9] Enumeration of rational plane curves tangent to a smooth cubic [J].

Cadman, Charles ;

Chen, Linda .

ADVANCES IN MATHEMATICS, 2008, 219 (01) :316-343

[10] Using stacks to impose tangency conditions on curves [J].

Cadman, Charles .

AMERICAN JOURNAL OF MATHEMATICS, 2007, 129 (02) :405-427

← 1 2 3 →