Journal de Mathématiques Pures et Appliquées ( IF 2.1 ) Pub Date : 2020-11-05 , DOI: 10.1016/j.matpur.2020.10.003 Andreas Leopold Knutsen
We prove that, for any , the étale double cover from the moduli space of complex polarized genus g Enriques surfaces to the moduli space of numerically polarized genus g Enriques surfaces is disconnected precisely over irreducible components of parametrizing 2-divisible classes, answering a question of Gritsenko and Hulek [13]. We characterize all irreducible components of in terms of a new invariant of line bundles on Enriques surfaces that generalizes the ϕ-invariant introduced by Cossec [8]. In particular, we get a one-to-one correspondence between the irreducible components of and 11-tuples of integers satisfying particular conditions. This makes it possible, in principle, to list all irreducible components of for each .
中文翻译:
在极化恩里克曲面的模空间上
我们证明,对于任何 ,étale双层封面 从模空间 极化极化g Enriques曲面对模空间的分布的数值偏振属克Enriques表面被断开的精确过束缚部件参数化2可除的类,回答了Gritsenko和Hulek的问题[13]。我们表征了所有不可约成分在上Enriques线束的新不变的术语表面,其概括了φ -invariant通过Cossec [8]引入。特别是,我们得到的不可约成分之间的一一对应关系和满足特定条件的11元整数。原则上,这使得列出所有不可约成分成为可能。 每个 。