Covering gonality of symmetric products of curves and Cayley–Bacharach condition on Grassmannians
Given an irreducible projective variety X, the covering gonality of X is the least gonality of an irreducible curve $E\subset X$ passing through a general point of X. In this paper, we study the covering gonality of the k-fold symmetric product $C^{(k)}$ of a smooth complex projective...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001002/type/journal_article |
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| Summary: | Given an irreducible projective variety X, the covering gonality of X is the least gonality of an irreducible curve
$E\subset X$
passing through a general point of X. In this paper, we study the covering gonality of the k-fold symmetric product
$C^{(k)}$
of a smooth complex projective curve C of genus
$g\geq k+1$
. It follows from a previous work of the first author that the covering gonality of the second symmetric product of C equals the gonality of C. Using a similar approach, we prove the same for the
$3$
-fold and the
$4$
-fold symmetric product of C. |
|---|---|
| ISSN: | 2050-5094 |