论文标题
分隔线和对数映射空间的曲线
Divisors and curves on logarithmic mapping spaces
论文作者
论文摘要
我们确定零属中稳定对数图的模量空间的理性类别和PICARD组，目标射击空间相对A超平面。对于班级组，我们表现出由边界除数组成的明确基础。对于PICARD组，我们展示了一个由热带化的分段线性函数索引的跨度集。在这两种情况下，通过从稳定曲线的空间中拉回WDVV关系，都可以获得一组完整的边界关系。我们的证明取决于对数映射空间中制造测试曲线的受控技术，打开了这些空间的拓扑结构，以进一步研究。
We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane. For the class group we exhibit an explicit basis consisting of boundary divisors. For the Picard group we exhibit a spanning set indexed by piecewise-linear functions on the tropicalisation. In both cases a complete set of boundary relations is obtained by pulling back the WDVV relations from the space of stable curves. Our proofs hinge on a controlled technique for manufacturing test curves in logarithmic mapping spaces, opening up the topology of these spaces to further study.
