论文标题
两个模量空间的故事：对数和多尺度差异
A tale of two moduli spaces: logarithmic and multi-scale differentials
论文作者
论文摘要
从平坦和复杂的几何学的角度，在[BCGGM3]中构建了多尺度差异，以压缩曲线的模量曲线，并与零件的差分和规定的零元素和极点。对数差异是在[MW20]中构建的，这是Gromov的稳定橡胶地图的概括 - Witten理论。 Modulo隔离了紧凑型的主要组成部分的全局残基条件，我们表明这两种差异是等效的，并建立了其（粗）模量堆栈的同构。此外，我们将橡胶和多尺度空间描述为在零属的情况下对稳定尖的有理曲线的模量空间的明确爆炸，并且是对任意属的发病率变化的全局爆炸，这意味着它们的投资性。我们还提出了与通用线束类相互作用的扭曲的霍奇束中的精制双分支周期公式。
Multi-scale differentials are constructed in [BCGGM3], from the viewpoint of flat and complex geometry, for the purpose of compactifying moduli spaces of curves together with a differential with prescribed orders of zeros and poles. Logarithmic differentials are constructed in [MW20], as a generalization of stable rubber maps from Gromov--Witten theory. Modulo the global residue condition that isolates the main components of the compactification, we show that these two kinds of differentials are equivalent, and establish an isomorphism of their (coarse) moduli stacks. Moreover, we describe the rubber and multi-scale spaces as an explicit blowup of the moduli space of stable pointed rational curves in the case of genus zero, and as a global blowup of the incidence variety compactification for arbitrary genera, which implies their projectivity. We also propose a refined double ramification cycle formula in the twisted Hodge bundle which interacts with the universal line bundle class.
