Abstract
In the paper (Markushevich et al., Cent Eur J Math 10:1331–1355, 2012) a conceptual description of compactifications of moduli spaces of stable vector bundles on surfaces has been given, whose boundaries consist of vector bundles on trees of surfaces. In this article a typical basic case for the projective plane is described explicitly including the construction of a relevant Kirwan blowup.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Eisenbud, D., Harris, J.: The Geometry of Schemes. Graduate Texts in Mathematics, vol. 197. Springer, New York (2001)
Harris, J.: Algebraic Geometry. Graduate Texts in Mathematics, vol. 133. Springer, New York (1992)
Hartshorne, R.: Algebraic Geometry. Springer, New York, Heidelberg, Berlin (1977)
Kirwan, F.: Partial desingularisations of quotients of nonsingular varieties and their Betti numbers. Ann. Math. 122, 41–85 (1985)
Markushevich, D., Tikhomirov, A.S., Trautmann, G.: Bubble tree compactification of moduli spaces of vector bundles on surfaces. Cent. Eur. J. Math. 10, 1331–1355 (2012)
Mumford, D., Fogarty, J.: Geometric Invariant Theory, 2nd enlarged edn. Springer, New York (1982)
Narasimhan, M.S., Trautmann, G.: Compactification of \(M_{P_{3}}(0,2)\) and Poncelet pairs of conics. Pac. J. Math. 145, 255–365 (1990)
Newstead, P.: Introduction to Moduli Problems and Orbit Spaces. Tata Institute Lectures, vol. 51, Springer (1978)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Trautmann, G. (2017). A Kirwan Blowup and Trees of Vector Bundles. In: Decker, W., Pfister, G., Schulze, M. (eds) Singularities and Computer Algebra. Springer, Cham. https://doi.org/10.1007/978-3-319-28829-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-28829-1_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28828-4
Online ISBN: 978-3-319-28829-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)