Towards an enumerative geometry of the moduli space of twisted curves and rth roots

By A. Chiodo. Compositio Mathematica, 2006

111 citations recorded by the source corpus.

Abstract The enumerative geometry of rth roots of line bundles is crucial in the theory of r-spin curves and occurs in the calculation of Gromov–Witten invariants of orbifolds. It requires the definition of the suitable compact moduli stack and the generalization of the standard techniques from the theory of moduli of stable curves. In a previous paper, we constructed a compact moduli stack by describing the notion of stability in the context of twisted curves. In this paper, by working with stable twisted curves, we extend Mumford’s formula for the Chern character of the Hodge bundle to the direct image of the universal rth root in K-theory.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/568e5fb1f93d966b8af7f6a04dff2f30a19a88a0

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

Equivalence of ELSV and Bouchard–Mariño conjectures for $$r$$r-spin Hurwitz numbers (2013, background): “Chiodo [7] studied the class S expressing it in terms of standard cohomology classes on the moduli space, the coefficients being equal to”
Double ramification cycles on the moduli spaces of curves (2016, background): “an, ξΓ,w: MΓ,w→M r,k g;a1,...,an . 24 Every factor in the last product is symmetric in hand h′ since Bm+1 w r = (−1)m+1B m+1 r−w r for m≥1. Proof. The Proposition follows from Chiodo’s formula [6] for the Chern characters of R∗π ∗L, chm(r,k;a1,...,an) = Bm+1( k r ) (m+1)! κm− Xn i=1 Bm+1( a i r )”