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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 18, Issue 2

Issues

Classification of degree two curves in the symmetric square with positive self-intersection

Meritxell Sáez
Published Online: 2018-01-31 | DOI: https://doi.org/10.1515/advgeom-2017-0046

Abstract

We give a precise classification of the pairs (C, ) with C a smooth curve of genus g and C(2) a curve of degree two and positive self-intersection. We prove that there are no such pairs if g < pa() < 2g−1. We study the singularities and self-intersection of any degree two curve in C(2). Moreover, we give examples of curves with arithmetic genus in the Brill–Noether range and positive self-intersection on C × C.

Keywords: Symmetric product; curve; irregular surface; curves in surfaces

MSC 2010: Primary 14H45; Secondary 14J25; 14H37; 14H10

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About the article


Received: 2015-08-25

Revised: 2016-02-11

Published Online: 2018-01-31

Published in Print: 2018-04-25


Funding: The author has been partially supported by the Proyecto de Investigación MTM2012-38122-C03-02.


Citation Information: Advances in Geometry, Volume 18, Issue 2, Pages 161–180, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0046.

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