论文标题
差异地层的非变化，仿射和极端几何形状
Nonvarying, affine, and extremal geometry of strata of differentials
论文作者
论文摘要
我们证明，[CM1，CM2]中阿贝尔和二次差异的非变化层具有微不足道的重言式环，并且是仿射品种。我们还证明，无限面积的$ k $ differentials是所有$ k $的仿射品种。由于这些仿射地层，因此在高于复数维度的程度上消失的同源性。此外，我们证明，有限区域的Abelian和二次差异的Hodge束的分层是极端的，因为在每个层中合并两个零会导致边界中的最大有效分裂。这些结果中的一个共同特征是差分层中除数类别以及在Teichmüller动力学中的化身的关系。
We prove that the nonvarying strata of abelian and quadratic differentials in [CM1, CM2] have trivial tautological rings and are affine varieties. We also prove that strata of $k$-differentials of infinite area are affine varieties for all $k$. Vanishing of homology in degree higher than the complex dimension follows as a consequence for these affine strata. Moreover we prove that the stratification of the Hodge bundle for abelian and quadratic differentials of finite area is extremal in the sense that merging two zeros in each stratum leads to an extremal effective divisor in the boundary. A common feature throughout these results is a relation of divisor classes in strata of differentials as well as its incarnation in Teichmüller dynamics.
