A Brief Introduction to Geometric Invariant Theory

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 240)


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.

Mathematics Subject Classification (2010)

Primary 14L24 Secondary 13A50 



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.


  1. 1.
    A. Borel, Linear algebraic groups, Springer-Verlag, New York, 1991.Google Scholar
  2. 2.
    I. Dolgachev, Lectures on invariant theory, Cambridge University Press, Cambridge, 2003.Google Scholar
  3. 3.
    I. V. Dolgachev and Y. Hu, Variation of geometric invariant theory quotients, Inst. Hautes Études Sci. Publ. Math. (1998), no. 87, 5–56.Google Scholar
  4. 4.
    J. Harris and I. Morrison, Moduli of curves, Springer-Verlag, New York, 1998.Google Scholar
  5. 5.
    R. Hartshorne, Algebraic geometry, Springer-Verlag, New York, 1977.Google Scholar
  6. 6.
    F. C. Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Mathematical Notes, Princeton University Press, Princeton, NJ, 1984.Google Scholar
  7. 7.
    D. Mumford, Stability of projective varieties, Enseignement Math. (2) 23 (1977), no. 1-2, 39–110.Google Scholar
  8. 8.
    D. Mumford, Geometric invariant theory, Springer-Verlag, 1982.Google Scholar
  9. 9.
    P. E. Newstead, Introduction to moduli problems and orbit spaces, Tata Institute of Fundamental Research, Bombay; by the Narosa Publishing House, New Delhi, 1978.Google Scholar
  10. 10.
    C. S. Seshadri, Quotient spaces modulo reductive algebraic groups, Ann. of Math. (2) 95 (1972), 511–556; errata, ibid. (2) 96 (1972), 599.Google Scholar
  11. 11.
    M. Thaddeus, Geometric invariant theory and flips, J. Amer. Math. Soc. 9 (1996), no. 3, 691–723.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityLansingUK
  2. 2.Department of Mathematics and StatisticsUniversity of New BrunswickFrederictonCanada

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