论文标题
唐纳森 - 托马斯（Thomas）的虚拟循环，calabi-yau不变4倍
Localizing virtual cycles for Donaldson-Thomas invariants of Calabi-Yau 4-folds
论文作者
论文摘要
最近，oh-thomas构建了一个虚拟周期$ [x]^{\ mathrm {\ mathrm {vir}} \在_*（x）$中，用于quasi-projective moduli space $ x $ x $ x $ x $ stable冰另皮带或复合物，或者在calabi-yau上构成了dt4 dovariants的calabi-yau 4倍，而dt4 dovariants可以定义ASENTELLES的组合级别。在本文中，我们证明虚拟周期本地定位于$ x $的阻塞支架$ ob_x $ of $ x $的同位素坐骨的$ x（σ）$，并构建一个本地化的虚拟周期$ [x]^{\ mathrm {vir}}}这是通过进一步定位的OH-Thomas类来实现的，该类别定位了Edidin-Graham的Square Root Euler类，该类别是特殊的正交捆绑包。当cosection $σ$被冲洗以使虚拟周期消失时，我们构造了一个简化的虚拟周期$ [x]^{\ mathrm {vir}} _ {\ mathrm {red}} $。作为应用程序，我们证明了Hyperkähler4倍的DT4消失结果。所有这些结果都适用于虚拟结构滑轮和K理论DT4不变性。
Recently Oh-Thomas constructed a virtual cycle $[X]^{\mathrm{vir}}\in A_*(X)$ for a quasi-projective moduli space $X$ of stable sheaves or complexes over a Calabi-Yau 4-fold against which DT4 invariants may be defined as integrals of cohomology classes. In this paper, we prove that the virtual cycle localizes to the zero locus $X(σ)$ of an isotropic cosection $σ$ of the obstruction sheaf $Ob_X$ of $X$ and construct a localized virtual cycle $[X]^{\mathrm{vir}}_{\mathrm{loc}}\in A_*(X(σ))$. This is achieved by further localizing the Oh-Thomas class which localizes Edidin-Graham's square root Euler class of a special orthogonal bundle. When the cosection $σ$ is surjective so that the virtual cycle vanishes, we construct a reduced virtual cycle $[X]^{\mathrm{vir}}_{\mathrm{red}}$. As an application, we prove DT4 vanishing results for hyperkähler 4-folds. All these results hold for virtual structure sheaves and K-theoretic DT4 invariants.
