论文标题
一堆可前的曲线堆果圈i
Chow rings of stacks of prestable curves I
论文作者
论文摘要
我们研究Moduli堆栈$ \ MATHFRAK {M} _ {G，N} $的Chow环，并在此堆栈上定义了重言式类别的概念。我们从模量空间的重言式环$ \ bar {\ mathcal {m}} _ {g，n} $稳定的稳定曲线的相交产物的公式和重言式类别的功能性。本文为本文第二部分提供了基础。 在附录（与J. Skowera的关节）中，我们发展了代数周期的适当但不是必要的投影性的理论。对于$ \ mathfrak {m} _ {g，n} $的重言式戒指的构建是必需的，并且本身就是重要的。我们还开发了代数堆栈的操作CHOW组。
We study the Chow ring of the moduli stack $\mathfrak{M}_{g,n}$ of prestable curves and define the notion of tautological classes on this stack. We extend formulas for intersection products and functoriality of tautological classes under natural morphisms from the case of the tautological ring of the moduli space $\bar{\mathcal{M}}_{g,n}$ of stable curves. This paper provides foundations for the second part of the paper. In the appendix (joint with J. Skowera), we develop the theory of a proper, but not necessary projective, pushforward of algebraic cycles. The proper pushforward is necessary for the construction of the tautological rings of $\mathfrak{M}_{g,n}$ and is important in its own right. We also develop operational Chow groups for algebraic stacks.
