Abstract
In this section we introduce the main objects of our study and recall the main results of [R1].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
As a section of \(\omega _{Z} \otimes \mathcal{O}_{X}(-L - K_{X})\).
- 2.
The inclusion \({\pi }^{{\ast}}\big{(}pr_{2{\ast}}\big{(}\mathcal{J}_{\mathcal{Z}}\otimes pr_{1}^{{\ast}}\mathcal{O}_{X}(L + K_{X})\big{)}\big{)} \subset \mathbf{\tilde{F}}_{i}\) is proved in [R1], Proposition 1.6.
- 3.
The self-duality of \(\tilde{\mathcal{F}}\) over Conf d (X) is provided by the quadratic form \(\mathbf{\tilde{q}}\) in (2.42).
References
E. Arbarello, M. Cornalba, P. Griffiths, J. Harris, in Geometry of Algebraic Curves, vol. I. Grundlehren der Mathematischen Wissenschafen, 267 (Springer, New York, 1985)
I. Reider, Nonabelian Jacobian of smooth projective surfaces. J. Differ. Geom. 74, 425–505 (2006)
A.N. Tyurin, Cycles, curves and vector bundles on an algebraic surface. Duke Math. J. 54, 1–26 (1987)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Reider, I. (2013). Nonabelian Jacobian J(X; L, d): Main Properties. In: Nonabelian Jacobian of Projective Surfaces. Lecture Notes in Mathematics, vol 2072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35662-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-35662-9_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35661-2
Online ISBN: 978-3-642-35662-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)