##### Department of Mathematics,

University of California San Diego

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### ENUMERATIVE GEOMETRY SEMINAR

## Nicola Tarasca

#### Virginia Commonwealth University

## Incident varieties of algebraic curves and canonical divisors

##### Abstract:

The theory of canonical divisors on curves has witnessed an explosion of interest in recent years, motivated by the recent developments in the study of limits of canonical divisors on nodal curves. Imposing conditions on canonical divisors allows one to construct natural geometric subvarieties of moduli spaces of pointed curves, called strata of canonical divisors. The strata are in fact the projection on moduli spaces of curves of incidence varieties in the projectivized Hodge bundle. I will present a graph formula for the class of the restriction of such incident varieties over the locus of pointed curves with rational tails. The formula is expressed as a linear combination of tautological classes indexed by decorated stable graphs, with coefficients enumerating appropriate weightings of decorated stable graphs. I will conclude with some applications. Joint work with Iulia Gheorghita.

### December 7, 2021

### 1:15 PM

Meeting ID: 915 4771 7800

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