A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves

被引：5

作者：

Battistella, Luca ^{[1
]}

Carocci, Francesca ^{[2
]}

机构：

[1] Humboldt Univ, Inst Math, Berlin, Germany

[2] Ecole Polytech Fed Lausanne, Inst Math, Lausanne, Switzerland

来源：

GEOMETRY & TOPOLOGY | 2023年 / 27卷 / 03期

基金：

欧洲研究理事会;

关键词：

GROMOV-WITTEN INVARIANTS; POINTED ELLIPTIC-CURVES; MODULAR COMPACTIFICATIONS; STABLE MAPS; SINGULARITIES; DEFORMATION; ENUMERATION; STACKS;

D O I：

10.2140/gt.2023.27.1203

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a modular desingularisation of (M) over bar (2,n)(P-r, d)(main). The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers; with this enhanced logarithmic structure, it is possible to desingularise the main component by means of a logarithmic modification. Both isolated and nonreduced singularities appear naturally. Our construction gives rise to a notion of reduced Gromov-Witten invariants in genus two.

引用

页码：1203 / 1272

页数：70

共 84 条

[61] Logarithmic geometry and algebraic stacks [J].