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Geometric Reductivity-A Quotient Space Approach


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1 Chennai Mathematical Institute, Plot No. H1, SIPCOT IT Park, Padur Post, Siruseri-603103, Kanchipuram District, India
     

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Mumford’s Geometric Invariant Theory or GIT is a major technique for finding quotients of algebraic schemes acted upon by reductive algebraic groups. It has been successful in finding solutions to moduli problems in the category of algebraic schemes. In the first edition (i.e., the 1965 edition) of Geometric Invariant Theory [13], Mumford restricted himself to algebraic schemes over fields of characteristic zero. In order to make his theory applicable over fields of arbitrary characteristic, he made the following conjecture in the Preface to the first edition of Ibid. (a conjecture subsequently proved by Haboush [5] in 1975).
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  • Geometric Reductivity-A Quotient Space Approach

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Authors

Pramathanath Sastry
Chennai Mathematical Institute, Plot No. H1, SIPCOT IT Park, Padur Post, Siruseri-603103, Kanchipuram District, India
C. S. Seshadri
Chennai Mathematical Institute, Plot No. H1, SIPCOT IT Park, Padur Post, Siruseri-603103, Kanchipuram District, India

Abstract


Mumford’s Geometric Invariant Theory or GIT is a major technique for finding quotients of algebraic schemes acted upon by reductive algebraic groups. It has been successful in finding solutions to moduli problems in the category of algebraic schemes. In the first edition (i.e., the 1965 edition) of Geometric Invariant Theory [13], Mumford restricted himself to algebraic schemes over fields of characteristic zero. In order to make his theory applicable over fields of arbitrary characteristic, he made the following conjecture in the Preface to the first edition of Ibid. (a conjecture subsequently proved by Haboush [5] in 1975).