Virtual wall crossing formulas for $C^*$-flips TeX Export

@article{citeulike:4695605, abstract = {Let \$M=[X/C^*]\$ be the quotient of a separated DM stack \$X\$ and let \$M\_\pm\$ be \$C^*\$-flips in \$M\$ which are open proper separated DM substacks. When \$M\$ is equipped with a perfect obstruction theory, the wall crossing seeks to find an explicit formula of the difference of virtual intersection numbers on \$M\_+\$ and \$M\_-\$. In this paper we provide a wall crossing formula by using a master space construction and the virtual localization theorem. When \$X\$ has an equivariant strongly symmetric obstruction theory, we construct an intrinsic blow-up of \$X\$ so that we can reduce the obstruction sheaf of the master space. Then we prove an explicit formula which calculates the wall crossing in terms of weights of the \$C^*\$ action on tangent spaces. Finally we apply this theorem to moduli spaces of sheaf complexes over a Calabi-Yau three-fold.}, archivePrefix = {arXiv}, author = {Kiem, Young-Hoon and Li, Jun}, citeulike-article-id = {4695605}, citeulike-linkout-0 = {http://arxiv.org/abs/0905.4770}, citeulike-linkout-1 = {http://arxiv.org/pdf/0905.4770}, day = {29}, eprint = {0905.4770}, keywords = {calabi\_yau, localization, virtual\_wall}, month = {May}, posted-at = {2009-11-10 04:59:09}, priority = {2}, title = {Virtual wall crossing formulas for \$C^*\$-flips}, url = {http://arxiv.org/abs/0905.4770}, year = {2009} }

TY - JOUR ID - citeulike:4695605 L3 - citeulike-article-id:4695605 N2 - Let $M=[X/C^*]$ be the quotient of a separated DM stack $X$ and let $M_\pm$ be $C^*$-flips in $M$ which are open proper separated DM substacks. When $M$ is equipped with a perfect obstruction theory, the wall crossing seeks to find an explicit formula of the difference of virtual intersection numbers on $M_+$ and $M_-$. In this paper we provide a wall crossing formula by using a master space construction and the virtual localization theorem. When $X$ has an equivariant strongly symmetric obstruction theory, we construct an intrinsic blow-up of $X$ so that we can reduce the obstruction sheaf of the master space. Then we prove an explicit formula which calculates the wall crossing in terms of weights of the $C^*$ action on tangent spaces. Finally we apply this theorem to moduli spaces of sheaf complexes over a Calabi-Yau three-fold. TI - Virtual wall crossing formulas for $C^*$-flips KW - calabi_yau KW - localization KW - virtual_wall AU - Kiem, Young-Hoon AU - Li, Jun PY - 2009/May/29/ UR - http://arxiv.org/abs/0905.4770 ER -