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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Effective cycles on the symmetric product of a curve, I: the diagonal cone


Authors: Francesco Bastianelli, Alexis Kouvidakis, Angelo Felice Lopez and Filippo Viviani; with an appendix by Ben Moonen
Journal: Trans. Amer. Math. Soc. 372 (2019), 8709-8758
MSC (2010): Primary 14C25, 14H51, 14C20
DOI: https://doi.org/10.1090/tran/7867
Published electronically: August 5, 2019
MathSciNet review: 4029710
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Abstract: In this paper we investigate the cone $ \operatorname {Pseff}_n(C_d)$ of pseudoeffective $ n$-cycles in the symmetric product $ C_d$ of a smooth curve $ C$. We study the convex-geometric properties of the cone $ \mathcal {D}_n(C_d)$ generated by the $ n$-dimensional diagonal cycles. In particular we determine its extremal rays and we prove that $ \mathcal {D}_n(C_d)$ is a perfect face of $ \operatorname {Pseff}_n(C_d)$ along which $ \operatorname {Pseff}_n(C_d)$ is locally finitely generated.


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Additional Information

Francesco Bastianelli
Affiliation: Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via Edoardo Orabona, 4, 70125 Bari, Italy
Email: francesco.bastianelli@uniba.it

Alexis Kouvidakis
Affiliation: Department of Mathematics and Applied Mathematics, University of Crete, GR-70013 Heraklion, Greece
Email: kouvid@math.uoc.gr

Angelo Felice Lopez
Affiliation: Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy
Email: lopez@mat.uniroma3.it

Filippo Viviani
Affiliation: Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy
Email: viviani@mat.uniroma3.it

Ben Moonen
Affiliation: Radboud University, IMAPP, P.O. Box 9010, 6500GL Nijmegen, The Netherlands
Email: b.moonen@science.ru.nl

DOI: https://doi.org/10.1090/tran/7867
Received by editor(s): June 11, 2018
Received by editor(s) in revised form: April 3, 2019
Published electronically: August 5, 2019
Additional Notes: Research partially supported by INdAM (GNSAGA) and by the MIUR national projects “Geometria delle varietà algebriche” PRIN 2010-2011 and “Spazi di moduli e applicazioni” FIRB 2012.
Article copyright: © Copyright 2019 American Mathematical Society