Incidence varieties in the projectivized kth Hodge bundle over curves with rational tails

Abstract

Over the moduli space of pointed smooth algebraic curves, the projectivized [Formula: see text]th Hodge bundle is the space of [Formula: see text]-canonical divisors. The incidence loci are defined by requiring the [Formula: see text]-canonical divisors to have prescribed multiplicities at the marked points. We compute the classes of the closure of the incidence loci in the projectivized [Formula: see text]th Hodge bundle over the moduli space of curves with rational tails. The classes are expressed as a linear combination of tautological classes indexed by decorated stable graphs with coefficients enumerating appropriate weightings. As a consequence, we obtain an explicit expression for some relations in tautological rings of moduli of curves with rational tails.