Logarithmic series and Hodge integrals in the tautological ring. With an appendix by Don Zagier.

By Carel Faber, R. Pandharipande. 2000

137 citations recorded by the source corpus.

0.1. Overview. Let Mg be the moduli space of Deligne–Mumford stable curves of genus g ≥ 2. The study of the Chow ring of the moduli space of curves was initiated by Mumford in [Mu]. In the past two decades, many remarkable properties of these intersection rings have been discovered. Our first goal in this paper is to describe a new perspective on the intersection theory of the moduli space of curves that encompasses advances from both classical degeneracy studies and topological gravity. This approach is developed in Sections 0.2–0.7. The main new results of the paper are computations of basic Hodge integral series in A∗(Mg) encoding the canonical evaluations of κg−2−iλi . The motivation for the study of these tautological elements and the series results are given in Section 0.8. The body of the paper contains the Hodge integral derivations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cd1fc43937970d28e0f863022a2ac59944829573

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

admcycles - a Sage package for calculations in the tautological ring of the moduli space of stable curves (2020, unknown): “For a detailed introduction to the tautological ring, see, e.g., [Faber and Pandharipande 2000; Arbarello et al. 2011; Pandharipande 2018].”
Relative maps and tautological classes (2003, methodology): “s in the subalgebras). A direct calculation shows: −π∗ ι∗([Mg,n] ×[M0,3]) 2 = ψi. Hence, the cotangent line classes lie in the tautological rings. A discussion of the κand λclasses can be found in [FP]. Gromov-Witten theory deﬁnes natural classes in A∗(Mg,n). Let Xbe a nonsingular projective variet”