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Transactions of the American Mathematical Society

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Classes of Weierstrass points on genus $ 2$ curves


Authors: Renzo Cavalieri and Nicola Tarasca
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 14H99; Secondary 14C99
DOI: https://doi.org/10.1090/tran/7626
Published electronically: May 20, 2019
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Abstract: We study the codimension $ n$ locus of curves of genus $ 2$ with $ n$ distinct marked Weierstrass points inside the moduli space of genus $ 2$, $ n$-pointed curves, for $ n \leq 6$. We give a recursive description of the classes of the closure of these loci inside the moduli space of stable curves. For $ n\leq 4$, we express these classes using a generating function over stable graphs indexing the boundary strata of moduli spaces of pointed stable curves. Similarly, we express the closure of these classes inside the moduli space of curves of compact-type for all $ n$. This is a first step in the study of the structure of hyperelliptic classes in all genera.


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Additional Information

Renzo Cavalieri
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
Email: renzo@math.colostate.edu

Nicola Tarasca
Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
Email: nicola.tarasca@rutgers.edu

DOI: https://doi.org/10.1090/tran/7626
Keywords: Effective cycles on moduli spaces of curves, the strata algebra, hyperelliptic curves.
Received by editor(s): November 12, 2017
Received by editor(s) in revised form: May 28, 2018
Published electronically: May 20, 2019
Article copyright: © Copyright 2019 American Mathematical Society