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DC Field | Value | Language |
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dc.contributor.author | Naranjo del Val, Juan Carlos | - |
dc.date.accessioned | 2023-05-02T06:25:14Z | - |
dc.date.available | 2023-05-02T06:25:14Z | - |
dc.date.issued | 1996-01-01 | - |
dc.identifier.issn | 0030-8730 | - |
dc.identifier.uri | http://hdl.handle.net/2445/197420 | - |
dc.description.abstract | Let $C$ be an irreducible complex smooth curve of genus $g ; \pi: \bar{C} \rightarrow C$ a connected unramified double covering of $C$. The Prym variety associated to the covering is, by definition, the component of the origin of the kernel of the norm $\operatorname{map} P(\bar{C}, C)=\operatorname{Ker}\left(\mathrm{Nm}_\pi\right)^0 \subset J \bar{C}$, that is, a principally polarized abelian variety (p.p.a.v.) of dimension $g(\bar{C})-g=g-1$. One defines the Prym map $P_g: \mathscr{R}_g \rightarrow \mathscr{A}_{g-1},(\bar{C} \stackrel{\pi}{\rightarrow} C) \mapsto P(\bar{C}, C)$, where $\mathscr{R}_g$ is the coarse moduli space of the coverings $\pi$ as above and $\mathscr{A}_{g-1}$ stands for the coarse moduli space of p.p.a.v.'s of dimension $g-1$. It is well known that this map is generically injective for $g \geq 7$. On the other hand, this map is never injective. The coarse moduli space $\mathscr{R} \mathscr{H}_g$ of and the fibres of the restriction of $P_g$ to $\mathscr{R} \mathscr{H}_g$ have positive dimension. Let $\mathscr{R}_g$ be the coarse moduli space of the unramified double coverings $\pi: \bar{C} \rightarrow C$ such that $C$ is a smooth bi-elliptic curve of genus $g$. This variety has $[(g+1) / 2]+2$ irreducible components: $\mathscr{R} \mathscr{B}_g=\left(\bigcup_{t=0}^{[(g-1) / 2]} \mathscr{R}_{g, t}\right) \cup \mathscr{R}_{\mathscr{B}_g^{\prime}}$. In this note the author characterizes the fibres of positive dimension of the Prym map. Theorem. Assume $g \geq 13$. A fibre of $P_g$ is positivedimensional at $(\bar{C}, C)$ if and only if $C$ is either hyperelliptic or $(\bar{C}, C) \in \bigcup_{t \geq 1} \mathscr{R}_{g, t}$. | - |
dc.format.extent | 4 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Mathematical Sciences Publishers | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.2140/pjm.1996.172.223 | - |
dc.relation.ispartof | Pacific Journal of Mathematics, 1996, vol. 172, num. 1, p. 223-226 | - |
dc.relation.uri | https://doi.org/10.2140/pjm.1996.172.223 | - |
dc.rights | (c) Mathematical Sciences Publishers, 1996 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Corbes algebraiques | - |
dc.subject.classification | Geometria algebraica | - |
dc.subject.classification | Varietats abelianes | - |
dc.subject.other | Algebraic curves | - |
dc.subject.other | Algebraic geometry | - |
dc.subject.other | Abelian varieties | - |
dc.title | The positive dimensional fibres of the Prym map | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 112660 | - |
dc.date.updated | 2023-05-02T06:25:14Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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112660.pdf | 404.26 kB | Adobe PDF | View/Open |
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