论文标题
Gromov-Witten/Hurwitz墙壁交叉
Gromov-Witten/Hurwitz wall-crossing
论文作者
论文摘要
对于目标品种$ x $和节点曲线$ c $，我们引入了一个参数稳定性条件，称为$ε$ - 可加权，用于从节点曲线到$ x \ times c $的地图。 If $X$ is a point, $ε$-admissibility interpolates between moduli spaces of stable maps to $C$ relative to some fixed points and moduli spaces of admissible covers with arbitrary ramifications over the same fixed points and simple ramifications elsewhere on $C$.使用周的纠缠尾巴，我们证明了与$ε$不同值的不变性的墙面横断公式。如果$ x $是一个表面，我们将这种墙面划线与作者的Quasimap墙壁交叉结合，以表明相对的pandharipande-thomas/gromov-witten $ x \ times c $ and ruan的对应关系，以及ruan的延长的毛皮动物的分辨率，$ x^{[n] $ tlical up up up up x^{[n] $ nas $ x^{x^^}墙壁交叉。因此，如果$ x $是折磨的del pezzo表面，我们就证明了三点属-0不变的三点属-0不变的猜想。
For a target variety $X$ and a nodal curve $C$, we introduce a one-parameter stability condition, termed $ε$-admissibility, for maps from nodal curves to $X\times C$. If $X$ is a point, $ε$-admissibility interpolates between moduli spaces of stable maps to $C$ relative to some fixed points and moduli spaces of admissible covers with arbitrary ramifications over the same fixed points and simple ramifications elsewhere on $C$. Using Zhou's entangled tails, we prove wall-crossing formulas relating invariants for different values of $ε$. If $X$ is a surface, we use this wall-crossing in conjunction with author's quasimap wall-crossing to show that the relative Pandharipande-Thomas/Gromov-Witten correspondence of $X\times C$ and Ruan's extended crepant resolution conjecture of the pair $X^{[n]}$ and $[X^{(n)}]$ are equivalent up to explicit wall-crossings. We thereby prove the crepant resolution conjecture for 3-point genus-0 invariants in all classes, if $X$ is a toric del Pezzo surface.
