论文标题
通过对数几何形状和戈伦斯坦曲线在投影空间中两曲线属的空间平滑压实
A smooth compactification of the space of genus two curves in projective space via logarithmic geometry and Gorenstein curves
论文作者
论文摘要
我们构建了$ \ overline {\ Mathcal {m}} _ {2，n}（\ Mathbb {p}^r，d）^{\ text {main}} $的模块化降低。两个属的戈伦斯坦奇异性的几何形状使我们考虑了可允许的可允许覆盖物中的地图：借助这种增强的对数结构，可以通过对数修改来使主要成分降低。孤立的和非还原的奇异性都自然而然。我们的构造产生了二属Gromov-witten不变性的概念。
We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced logarithmic structure, it is possible to desingularise the main component by means of a logarithmic modification. Both isolated and non-reduced singularities appear naturally. Our construction gives rise to a notion of reduced Gromov-Witten invariants in genus two.
