## Rank-two vector bundles on non-minimal ruled surfaces

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- by Marian Aprodu, Laura Costa and Rosa Maria Miró-Roig PDF
- Trans. Amer. Math. Soc.
**370**(2018), 3913-3929 Request permission

## 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.## References

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## Additional Information

**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
- MR Author ID: 611558
- 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
- MR Author ID: 125375
- ORCID: 0000-0003-1375-6547
- Email: miro@ub.edu
- 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 - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**370**(2018), 3913-3929 - MSC (2010): Primary 14F05; Secondary 14D20
- DOI: https://doi.org/10.1090/tran/7062
- MathSciNet review: 3811514