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Geometric invariant theory and flips
 Jour. AMS
, 1996
"... Ever since the invention of geometric invariant theory, it has been understood that the quotient it constructs is not entirely canonical, but depends on a choice: the choice of a linearization of the group action. However, the founders of the subject never made a systematic study of this dependence. ..."
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Cited by 141 (4 self)
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Ever since the invention of geometric invariant theory, it has been understood that the quotient it constructs is not entirely canonical, but depends on a choice: the choice of a linearization of the group action. However, the founders of the subject never made a systematic study of this dependence
GEOMETRIC INVARIANT THEORY
, 2012
"... Geometric Invariant Theory is the study of quotients in the context of algebraic geometry. Many objects we would wish to take a quotient of have some sort of geometric structure and Geometric Invariant Theory (GIT) allows us to construct quotients that preserve geometric structure. Quotients are nat ..."
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Geometric Invariant Theory is the study of quotients in the context of algebraic geometry. Many objects we would wish to take a quotient of have some sort of geometric structure and Geometric Invariant Theory (GIT) allows us to construct quotients that preserve geometric structure. Quotients
Heights and geometric invariant theory
 Forum Mathematicum
"... Abstract. Let K be a number field, OK be its ring of integers. We introduce the notion of compactified representation of GLN(OK) and, we see how to associate to a hermitian vector bundle E over Spec(OK) and a compactified representation T, a hermitian tensor bundle ET. We can prove then that there e ..."
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Cited by 3 (0 self)
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height theory and geometric invariant theory. In particular J.B. Bost [Bo1] and S. Zhang [Zh2] shown that, if X ⊂ P N (Q) is a closed variety which has SL(N + 1)–
On small geometric invariants of
"... Abstract. A small geometric invariant is a nonnegative integer invariant associated with a 3manifold whose value is bounded above by the Heegaard genus of the manifold. Craggs has studied techniques to detect for a given 3manifold M 3, whether the double 2M = Bd(M ⋆ ×[−1, 1]) bounds a 4manifold N ..."
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Abstract. A small geometric invariant is a nonnegative integer invariant associated with a 3manifold whose value is bounded above by the Heegaard genus of the manifold. Craggs has studied techniques to detect for a given 3manifold M 3, whether the double 2M = Bd(M ⋆ ×[−1, 1]) bounds a 4manifold
Geometric invariants of fanning curves
 Adv. Appl. Math
"... Abstract. We study the geometry of an important class of generic curves in the Grassmann manifolds of ndimensional subspaces and Lagrangian subspaces of IR 2n under the action of the linear and linear symplectic groups. ..."
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Abstract. We study the geometry of an important class of generic curves in the Grassmann manifolds of ndimensional subspaces and Lagrangian subspaces of IR 2n under the action of the linear and linear symplectic groups.
Geometric invariant theory . . .
, 2005
"... We define projective GIT quotients, and introduce toric varieties from this perspective. We illustrate the definitions by exploring the relationship between toric varieties and polyhedra. ..."
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We define projective GIT quotients, and introduce toric varieties from this perspective. We illustrate the definitions by exploring the relationship between toric varieties and polyhedra.
SITE CHARACTERIZATIONS FOR GEOMETRIC INVARIANTS OF TOPOSES
"... Abstract. We discuss the problem of characterizing the property of a Grothendieck topos to satisfy a given ‘geometric ’ invariant as a property of its sites of definition, and indicate a set of general techniques for establishing such criteria. We then apply our methodologies to specific invariants, ..."
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Abstract. We discuss the problem of characterizing the property of a Grothendieck topos to satisfy a given ‘geometric ’ invariant as a property of its sites of definition, and indicate a set of general techniques for establishing such criteria. We then apply our methodologies to specific invariants
GEOMETRIC INVARIANT THEORY AND BIRATIONAL GEOMETRY
, 2005
"... ABSTRACT. In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weak Factorization Theorems of nonsingular projective varieties and more generally projective varieties with fin ..."
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ABSTRACT. In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weak Factorization Theorems of nonsingular projective varieties and more generally projective varieties
Geometric Invariant Theory and EinsteinWeyl Geometry
, 2006
"... In this article, we review the Geometric Invariant Theory for Toric Varieties and present an application of it to EinsteinWeyl Geometry 1 ..."
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In this article, we review the Geometric Invariant Theory for Toric Varieties and present an application of it to EinsteinWeyl Geometry 1
Results 1  10
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