Brill-Noether loci in codimension two
classification
🧮 math.AG
keywords
curvesbrill-noethercodimensionlocusmodulispaceclassclosure
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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.
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