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Transactions of the American Mathematical Society

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

 
 

 

Rank-two vector bundles on non-minimal ruled surfaces


Authors: Marian Aprodu, Laura Costa and Rosa Maria Miró-Roig
Journal: Trans. Amer. Math. Soc. 370 (2018), 3913-3929
MSC (2010): Primary 14F05; Secondary 14D20
DOI: https://doi.org/10.1090/tran/7062
Published electronically: December 27, 2017
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Abstract: We continue previous work by various authors and study the birational geometry of moduli spaces of stable rank-two vector bundles on surfaces with Kodaira dimension $ -\infty $. To this end, we express vector bundles as natural extensions by using two numerical invariants associated to vector bundles, similar to the invariants defined by Brînzănescu and Stoia in the case of minimal surfaces. We compute explicitly these natural extensions on blowups of general points on a minimal surface. In the case of rational surfaces, we prove that any irreducible component of a moduli space is either rational or stably rational.


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Marian Aprodu
Affiliation: Facultatea de Matematică şi Informatică, Universitatea din Bucureşti, Str. Academiei 14, 010014 Bucureşti, Romania – and – Institutul de Matematică “Simion Stoilow” al Academiei Române, Calea Griviţei 21, Sector 1, 010702 Bucureşti, Romania
Email: marian.aprodu@fmi.unibuc.ro, marian.aprodu@imar.ro

Laura Costa
Affiliation: Facultat de Matemàtiques i Informàtica, Departament de Matemàtiques i Informàtica, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
Email: costa@ub.edu

Rosa Maria Miró-Roig
Affiliation: Facultat de Matemàtiques i Informàtica, Departament de Matemàtiques i Informàtica, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
Email: miro@ub.edu

DOI: https://doi.org/10.1090/tran/7062
Received by editor(s): March 30, 2016
Received by editor(s) in revised form: September 1, 2016
Published electronically: December 27, 2017
Additional Notes: The first author was partially supported by UEFISCDI Grant PN-II-PCE-2011-3-0288
The second author was partially supported by MTM2016-78623-P
The third author was partially supported by MTM2016-78623-P
Article copyright: © Copyright 2017 American Mathematical Society

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