论文标题
Orbifold Gromov-加权爆炸理论
Orbifold Gromov--Witten theory of weighted blowups
论文作者
论文摘要
考虑一个紧凑型sub-Orbifold groupoid $ \ sf s $的紧凑型符号oRbifold groupoid $（\ mathsf x，ω）$。令$ \ mathsf x _ {\ mathfrak a} $为重量 - $ \ mathfrak a $ \ sf x $沿$ \ sf s $沿$ \ sf s $，以及$ \ m m缩$ \ sf x $的$ \ sf s $。在本文中，我们表明，$ \ mathsf x _ {\ mathfrak a} $的绝对orbifold gromov-可以有效地从绝对的Orbifold Gromov- $ \ sf x $，$ \ sf s $ \ sf s $ s $和$ \ mathsf d horther a plantim a phloak a phortiast A { $ h^*_ {\ text {cr}}（{\ sf x}）\ rightArrow h^*_ {\ text {cr}}}（{\ sf s}）$和$ \ mathsf d _ {\ mathsf d _ {\ mathfrak a} $的$ \ mathsf d _} $的chern chern类班级。为了实现这一目标，我们首先证明了相对的Orbifold Gromov- $（\ Mathsf X _ {\ Mathfrak a} | \ Mathsf D _ {\ Mathfrak a}）$和$（\ Mathsf N _ _ {\ Mathfrak a} | \ Mathsf D _ = \ MathAR）作为这些结果的应用，我们证明了毛利克猜想的构造版本 - 沿着格罗莫夫（Gromov） - 沿着完整交叉点的爆炸理论，对gromov的构建理论 - 对根构建理论的猜想，并在leray-hirsch on leray-hirsch romov gromov gromov gromov gromov gromov- hirsch gromov--
Consider a compact symplectic sub-orbifold groupoid $\sf S$ of a compact symplectic orbifold groupoid $(\mathsf X,ω)$. Let $\mathsf X_{\mathfrak a}$ be the weight-$\mathfrak a$ blowup of $\sf X$ along $\sf S$, and $\mathsf D_{\mathfrak a}=\mathsf{PN}_{\mathfrak a}$ be the exceptional divisor, where $\sf N$ is the normal bundle of $\sf S$ in $\sf X$. In this paper we show that the absolute orbifold Gromov--Witten theory of $\mathsf X_{\mathfrak a}$ can be effectively and uniquely reconstructed from the absolute orbifold Gromov--Witten theories of $\sf X$, $\sf S$ and $\mathsf D_{\mathfrak a}$, the natural restriction homomorphism $H^*_{\text{CR}}({\sf X})\rightarrow H^*_{\text{CR}}({\sf S})$ and the first Chern class of the tautological line bundle over $\mathsf D_{\mathfrak a}$. To achieve this we first prove similar results for the relative orbifold Gromov--Witten theories of $(\mathsf X_{\mathfrak a}|\mathsf D_{\mathfrak a})$ and $(\mathsf N_{\mathfrak a}|\mathsf D_{\mathfrak a})$. As applications of these results, we prove an orbifold version of a conjecture of Maulik--Pandharipande on the Gromov--Witten theory of blowups along complete intersections, a conjecture on the Gromov--Witten theory of root constructions and a conjecture on Leray--Hirsch result for orbifold Gromov--Witten theory of Tseng--You.
