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1,026
The homogeneous coordinate ring of a toric variety
, 1992
"... This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each onedimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes in the Chow group An−1(X) of ..."
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Cited by 474 (7 self)
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This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each onedimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes in the Chow group An−1(X
Toric Varieties and Toric Resolutions
"... This paper is an introduction to toric varieties and toric resolutions. We begin with basic denitions and examples, and then cover standard topics in toric geometry, including fans, support functions, and ampleness criteria. The paper also explores alternate constructions of toric varieties and n ..."
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Cited by 8 (0 self)
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This paper is an introduction to toric varieties and toric resolutions. We begin with basic denitions and examples, and then cover standard topics in toric geometry, including fans, support functions, and ampleness criteria. The paper also explores alternate constructions of toric varieties
Derived categories of toric varieties
 Michigan Math. J
"... The purpose of this paper is to investigate the structure of the derived categories of toric varieties. We shall prove the following: ..."
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Cited by 51 (2 self)
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The purpose of this paper is to investigate the structure of the derived categories of toric varieties. We shall prove the following:
Frobenius splittings of toric varieties
 ALGEBRA NUMBER THEORY
, 2008
"... We discuss a characteristic free version of Frobenius splittings for toric varieties and give a polyhedral criterion for a toric variety to be diagonally split. We apply this criterion to show that section rings of nef line bundles on diagonally split toric varieties are normally presented and Kosz ..."
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Cited by 5 (1 self)
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We discuss a characteristic free version of Frobenius splittings for toric varieties and give a polyhedral criterion for a toric variety to be diagonally split. We apply this criterion to show that section rings of nef line bundles on diagonally split toric varieties are normally presented
Notes on toric varieties
, 2002
"... These notes survey some basic results in toric varieties over a field F, with examples and applications. A computer algebra package (written by the author) is described which deals with both affine and projective toric varieties in any number of dimensions (written in both MAGMA [MAGMA] and GAP [GAP ..."
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These notes survey some basic results in toric varieties over a field F, with examples and applications. A computer algebra package (written by the author) is described which deals with both affine and projective toric varieties in any number of dimensions (written in both MAGMA [MAGMA] and GAP
On the Brauer group of toric varieties
"... Toric varieties are a special class of rational varieties defined by equations of the form monomial = monomial. For a good brief survey of the history and role of toric varieties see [10]. Any toric variety X contains a cover by affine open sets described in terms of arrangements (called fans) of co ..."
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Cited by 12 (6 self)
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Toric varieties are a special class of rational varieties defined by equations of the form monomial = monomial. For a good brief survey of the history and role of toric varieties see [10]. Any toric variety X contains a cover by affine open sets described in terms of arrangements (called fans
Combinatorics and quotients of toric varieties
 Discrete Comput. Geom
, 2002
"... This paper studies two related subjects. One is some combinatorics arising from linear projections of polytopes and fans of cones. The other is quotient varieties of toric varieties. The relation is that projections of polytopes are related to quotients of projective toric varieties and projection o ..."
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Cited by 5 (0 self)
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This paper studies two related subjects. One is some combinatorics arising from linear projections of polytopes and fans of cones. The other is quotient varieties of toric varieties. The relation is that projections of polytopes are related to quotients of projective toric varieties and projection
Koszul duality for toric varieties
, 2003
"... Abstract. We show that certain categories of perverse sheaves on affine toric varieties Xσ and Xσ ∨ defined by dual cones are Koszul dual in the sense of Beilinson, Ginzburg and Soergel [BGS]. The functor expressing this duality is constructed explicitly using a combinatorial model for mixed sheaves ..."
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Cited by 3 (0 self)
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Abstract. We show that certain categories of perverse sheaves on affine toric varieties Xσ and Xσ ∨ defined by dual cones are Koszul dual in the sense of Beilinson, Ginzburg and Soergel [BGS]. The functor expressing this duality is constructed explicitly using a combinatorial model for mixed
HOMOGENEOUS TORIC VARIETIES
, 2009
"... A description of transitive actions of a semisimple algebraic group G on toric varieties is obtained. Every toric variety admitting such an action lies between a product of punctured affine spaces and a product of projective spaces. The result is based on the Cox realization of a toric variety as a ..."
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Cited by 3 (0 self)
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A description of transitive actions of a semisimple algebraic group G on toric varieties is obtained. Every toric variety admitting such an action lies between a product of punctured affine spaces and a product of projective spaces. The result is based on the Cox realization of a toric variety
Results 1  10
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1,026