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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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001002/type/journal_article |
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| author | Francesco Bastianelli Nicola Picoco |
| author_facet | Francesco Bastianelli Nicola Picoco |
| author_sort | Francesco Bastianelli |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1e9eccfb38634c69acaa69f0c4cc4c5b |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-1e9eccfb38634c69acaa69f0c4cc4c5b2025-01-24T05:20:08ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2024.100Covering gonality of symmetric products of curves and Cayley–Bacharach condition on GrassmanniansFrancesco Bastianelli0https://orcid.org/0000-0002-6684-4041Nicola Picoco1Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via Edoardo Orabona 4, 70125 Bari, ItalyDipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via Edoardo Orabona 4, 70125 Bari, Italy; E-mail: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.https://www.cambridge.org/core/product/identifier/S2050509424001002/type/journal_article14E9914E0814H5114N05 |
| spellingShingle | Francesco Bastianelli Nicola Picoco Covering gonality of symmetric products of curves and Cayley–Bacharach condition on Grassmannians Forum of Mathematics, Sigma 14E99 14E08 14H51 14N05 |
| title | Covering gonality of symmetric products of curves and Cayley–Bacharach condition on Grassmannians |
| title_full | Covering gonality of symmetric products of curves and Cayley–Bacharach condition on Grassmannians |
| title_fullStr | Covering gonality of symmetric products of curves and Cayley–Bacharach condition on Grassmannians |
| title_full_unstemmed | Covering gonality of symmetric products of curves and Cayley–Bacharach condition on Grassmannians |
| title_short | Covering gonality of symmetric products of curves and Cayley–Bacharach condition on Grassmannians |
| title_sort | covering gonality of symmetric products of curves and cayley bacharach condition on grassmannians |
| topic | 14E99 14E08 14H51 14N05 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001002/type/journal_article |
| work_keys_str_mv | AT francescobastianelli coveringgonalityofsymmetricproductsofcurvesandcayleybacharachconditionongrassmannians AT nicolapicoco coveringgonalityofsymmetricproductsofcurvesandcayleybacharachconditionongrassmannians |