Characterization of curves in C(2)

Meritxell Sáez

doi:10.1007/s13348-015-0147-x

Characterization of curves in C⁽²⁾

Meritxell Sáez^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

In this paper we characterize the irreducible curves lying in C⁽²⁾. We prove that a curve B has a degree one morphism to C⁽²⁾ with image a curve of degree d, with irreducible preimage in C× C, if and only if there exists an irreducible smooth curve D and morphisms from D to C and B, of degrees d and 2 respectively, forming a diagram which does not reduce.

Original language	English
Pages (from-to)	399-405
Number of pages	7
Journal	Collectanea Mathematica
Volume	67
Issue number	3
DOIs	https://doi.org/10.1007/s13348-015-0147-x
Publication status	Published - 1 Sept 2016
Externally published	Yes

Keywords

Curve
Curves in surfaces
Irregular surface
Symmetric product

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10.1007/s13348-015-0147-x

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abstract = "In this paper we characterize the irreducible curves lying in C(2). We prove that a curve B has a degree one morphism to C(2) with image a curve of degree d, with irreducible preimage in C× C, if and only if there exists an irreducible smooth curve D and morphisms from D to C and B, of degrees d and 2 respectively, forming a diagram which does not reduce.",

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AB - In this paper we characterize the irreducible curves lying in C(2). We prove that a curve B has a degree one morphism to C(2) with image a curve of degree d, with irreducible preimage in C× C, if and only if there exists an irreducible smooth curve D and morphisms from D to C and B, of degrees d and 2 respectively, forming a diagram which does not reduce.

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KW - Curves in surfaces

KW - Irregular surface

KW - Symmetric product

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Characterization of curves in C⁽²⁾

Abstract

Keywords

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