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arXiv · 2106.15637

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

Iulia Gheorghita·Nicola Tarasca
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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.

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Iulia Gheorghita, Nicola Tarasca. 2021-06-29. Incidence varieties in the projectivized $k$-th Hodge bundle over curves with rational tails. https://doi.org/10.1142/s0219199723500153

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