Abstract
Abstract
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
$\overline {\mathcal {M}}_{g,n}$
of stable curves. This paper provides foundations for the paper [BS21].
In the appendix (jointly 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.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Reference32 articles.
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