Characterization of C(n)

Meritxell Saéz

doi:10.1017/nmj.2016.13

Characterization of C⁽ⁿ⁾

Meritxell Saéz^*

^*Corresponding author for this work

Research output: Indexed journal article › Article › peer-review

Abstract

In this paper a new geometric characterization of the th symmetric product of a curve is given. Specifically, we assume that there exists a chain of smooth subvarieties V_i of dimension i, such that V_i is an ample divisor in V_i+1 and its intersection product with V₁ is one; that the Albanese dimension of V₂ is 2 and the genus of is equal to the irregularity of the variety. We prove that in this case the variety is isomorphic to the symmetric product of a curve.

Original language	English
Pages (from-to)	1-9
Number of pages	9
Journal	Nagoya Mathematical Journal
Volume	224
DOIs	https://doi.org/10.1017/nmj.2016.13
Publication status	Published - 1 Dec 2016
Externally published	Yes

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10.1017/nmj.2016.13

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abstract = "In this paper a new geometric characterization of the th symmetric product of a curve is given. Specifically, we assume that there exists a chain of smooth subvarieties Vi of dimension i, such that Vi is an ample divisor in Vi+1 and its intersection product with V1 is one; that the Albanese dimension of V2 is 2 and the genus of is equal to the irregularity of the variety. We prove that in this case the variety is isomorphic to the symmetric product of a curve.",

author = "Meritxell Sa{\'e}z",

note = "Funding Information: The author thanks Miguel Angel Barja and Joan Carles Naranjo for the multiple discussions and invaluable help on the development of this article. Many thanks also to the Universitat de Barcelona for the pre-doctoral grant APIF and their hospitality afterward. Publisher Copyright: {\textcopyright} 2016 by The Editorial Board of the Nagoya Mathematical Journal.",

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N2 - In this paper a new geometric characterization of the th symmetric product of a curve is given. Specifically, we assume that there exists a chain of smooth subvarieties Vi of dimension i, such that Vi is an ample divisor in Vi+1 and its intersection product with V1 is one; that the Albanese dimension of V2 is 2 and the genus of is equal to the irregularity of the variety. We prove that in this case the variety is isomorphic to the symmetric product of a curve.

AB - In this paper a new geometric characterization of the th symmetric product of a curve is given. Specifically, we assume that there exists a chain of smooth subvarieties Vi of dimension i, such that Vi is an ample divisor in Vi+1 and its intersection product with V1 is one; that the Albanese dimension of V2 is 2 and the genus of is equal to the irregularity of the variety. We prove that in this case the variety is isomorphic to the symmetric product of a curve.

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ER -

Characterization of C⁽ⁿ⁾

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