The moduli space of stable quotients
The moduli space of stable quotients
复制标题
DOI：
10.2140/gt.2011.15.1651
复制
发表时间：
2009-04
影响因子：
2
通讯作者：
A. Marian;D. Oprea;R. Pandharipande
中科院分区：
文献类型：
--
作者：
A. Marian;D. Oprea;R. Pandharipande
引入了稳定曲线上秩为n的平凡层的稳定子的模空间。在非奇异曲线上，模空间是Grothendieck的Quot方案。在节点曲线上，构造了一个相对的结构，使商的挠率远离奇点。经典空间的新紧化自然产生：得到了亏格为1的曲线到射影空间的映射的模的非奇异不可约紧化。在稳定同分模上的局部化导致重言式环中的新关系，推广了Brill-Noether结构。证明了稳定子的模空间携带一个规范的2项阻塞理论，因此是一个虚类。由此产生的系统的后裔不变量被证明是平等的格罗莫夫维滕理论的格拉斯曼在所有的属。稳定商也可用于研究卡拉比-丘几何。计算出的圆锥形与稳定映射一致。提出了关于稳定子对任意目标的行为的几个问题。14 N35; 14 C17献给威廉·富尔顿70岁生日
A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck’s Quot scheme. Over nodal curves, a relative construction is made to keep the torsion of the quotient away from the singularities. New compactifications of classical spaces arise naturally: a nonsingular and irreducible compactification of the moduli of maps from genus 1 curves to projective space is obtained. Localization on the moduli of stable quotients leads to new relations in the tautological ring generalizing Brill‐Noether constructions. The moduli space of stable quotients is proven to carry a canonical 2‐term obstruction theory and thus a virtual class. The resulting system of descendent invariants is proven to equal the Gromov‐Witten theory of the Grassmannian in all genera. Stable quotients can also be used to study Calabi‐Yau geometries. The conifold is calculated to agree with stable maps. Several questions about the behavior of stable quotients for arbitrary targets are raised. 14N35; 14C17 Dedicated to William Fulton on the occasion of his 70th birthday