论文标题
在Abelian差异的模量空间的Kodaira尺寸上
On the Kodaira dimension of moduli spaces of Abelian differentials
论文作者
论文摘要
本文为确定大属中规定的零和极阶的Abelian差异层的kodaira维度奠定了基础。我们与[BCGGM2]中构建的多尺度差异的模量空间合作，该空间提供了这些层的Orbifold紧凑型。我们建立了多尺度差异的模量空间的预测性，描述了规范奇异性的轨迹，并计算一系列有效的除数类别。此外，我们表现出规范类别的扰动，该类别允许相应的孤立形式形式延伸到非典型奇点的轨迹上。 作为应用，我们在G足够大的情况下对具有很少的零零和具有等分分配的零订单的地层以及地层进行了认证。特别是，我们显示了G> 12的最小地层的奇数旋转成分的一般类型。
This paper lays the foundation for determining the Kodaira dimension of the projectivized strata of Abelian differentials with prescribed zero and pole orders in large genus. We work with the moduli space of multi-scale differentials constructed in [BCGGM2] which provides an orbifold compactification of these strata. We establish the projectivity of the moduli space of multi-scale differentials, describe the locus of canonical singularities, and compute a series of effective divisor classes. Moreover, we exhibit a perturbation of the canonical class which allows the corresponding pluri-canonical forms to extend over the locus of non-canonical singularities. As applications, we certify general type for strata with few zeros as well as for strata with equidistributed zero orders when g is sufficiently large. In particular, we show general type for the odd spin components of the minimal strata for g > 12.
