Incidence varieties in the projectivized $k$-th Hodge bundle over curves with rational tails

Abstract

Over the moduli space of pointed smooth algebraic curves, the projectivized $k$-th Hodge bundle is the space of $k$-canonical divisors. The incidence loci are defined by requiring the $k$-canonical divisors to have prescribed multiplicities at the marked points. We compute the classes of the closure of the incidence loci in the projectivized $k$-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.

46 pages + appendix

References in corpus (5)

• Compactification of strata of abelian differentials
• The moduli space of twisted canonical divisors
• Relations on ${\overline{M}}_{g,n}$ via equivariant Gromov-Witten theory of ${\mathbb{P}}^1$
• Cohomology classes of strata of differentials
• Extremality of loci of hyperelliptic curves with marked Weierstrass points