Abstract
We provide a brief introduction to Geometric Invariant Theory. Specifically, we discuss some foundational concepts and results and illustrate the general theory by way of examples.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Borel, Linear algebraic groups, Springer-Verlag, New York, 1991.
I. Dolgachev, Lectures on invariant theory, Cambridge University Press, Cambridge, 2003.
I. V. Dolgachev and Y. Hu, Variation of geometric invariant theory quotients, Inst. Hautes Études Sci. Publ. Math. (1998), no. 87, 5–56.
J. Harris and I. Morrison, Moduli of curves, Springer-Verlag, New York, 1998.
R. Hartshorne, Algebraic geometry, Springer-Verlag, New York, 1977.
F. C. Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Mathematical Notes, Princeton University Press, Princeton, NJ, 1984.
D. Mumford, Stability of projective varieties, Enseignement Math. (2) 23 (1977), no. 1-2, 39–110.
D. Mumford, Geometric invariant theory, Springer-Verlag, 1982.
P. E. Newstead, Introduction to moduli problems and orbit spaces, Tata Institute of Fundamental Research, Bombay; by the Narosa Publishing House, New Delhi, 1978.
C. S. Seshadri, Quotient spaces modulo reductive algebraic groups, Ann. of Math. (2) 95 (1972), 511–556; errata, ibid. (2) 96 (1972), 599.
M. Thaddeus, Geometric invariant theory and flips, J. Amer. Math. Soc. 9 (1996), no. 3, 691–723.
Acknowledgements
The author was financially supported by an AARMS postdoctoral fellowship at the University of New Brunswick. The author also thanks the organizers of the PIMS Superschool on derived categories and D-branes for asking him to give an introductory lecture about GIT and also for suggesting a possible list of topics to cover.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Grieve, N. (2018). A Brief Introduction to Geometric Invariant Theory. In: Ballard, M., Doran, C., Favero, D., Sharpe, E. (eds) Superschool on Derived Categories and D-branes. SDCD 2016. Springer Proceedings in Mathematics & Statistics, vol 240. Springer, Cham. https://doi.org/10.1007/978-3-319-91626-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-91626-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91625-5
Online ISBN: 978-3-319-91626-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)