A generalization of the double ramification cycle via log-geometry
A generalization of the double ramification cycle via log-geometry
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通过对数几何对双分支循环的推广
DOI：
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发表时间：
2016
期刊：
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通讯作者：
J'er'emy Gu'er'e
中科院分区：
文献类型：
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作者：
J'er'emy Gu'er'e
本文给出了Farkas-Pandharipande构造的扭正则因子空间的对数几何描述。特别是，我们引入了一个主要的橡胶$k$-对数典型因子的概念，我们研究了它的模空间。它是一个适当的Deligne-Mumford栈，它承认一个理想的阻塞理论，其虚基本循环的维数为2g-3+n。在k=1的严格亚纯情形下，模空间具有期望维数，其虚基本环到稳定曲线模空间的前推等于扭标准因子模空间的加权基本类.在猜想上，给出了稳定曲线模空间中二重分歧环的推广的Pixton公式。
We give a log-geometric description of the space of twisted canonical divisors constructed by Farkas--Pandharipande. In particular, we introduce the notion of a principal rubber $k$-log-canonical divisor, and we study its moduli space. It is a proper Deligne--Mumford stack admitting a perfect obstruction theory whose virtual fundamental cycle is of dimension $2g-3+n$. In the so-called strictly meromorphic case with $k=1$, the moduli space is of the expected dimension and the push-forward of its virtual fundamental cycle to the moduli space of stable curves equals the weighted fundamental class of the moduli space of twisted canonical divisors. Conjecturally, it yields a formula of Pixton generalizing the double ramification cycle in the moduli space of stable curves.