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Brill–Noether loci in codimension two

Part of: Curves

Published online by Cambridge University Press:  07 August 2013

Nicola Tarasca
Nicola Tarasca*
Affiliation:
Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany email [email protected]
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Abstract

Let us consider the locus in the moduli space of curves of genus $2k$ defined by curves with a pencil of degree $k$. Since the Brill–Noether number is equal to $- 2$, such a locus has codimension two. Using the method of test surfaces, we compute the class of its closure in the moduli space of stable curves.

Keywords

moduli of curvesBrill–Noether theory

MSC classification

Secondary: 14H10: Families, moduli (algebraic) 14H51: Special divisors (gonality, Brill-Noether theory)
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 9 , September 2013 , pp. 1535 - 1568
Copyright
© The Author(s) 2013 

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