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Examples and Counterexamples of Existence of Categorical Quotients
 J. ALGEBRA
, 1999
"... In the setting of subtorus actions on toric varieties, we give examples for existence and nonexistence of categorical quotients for algebraic group actions in the categories of algebraic varieties and algebraic prevarieties. ..."
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Cited by 11 (7 self)
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In the setting of subtorus actions on toric varieties, we give examples for existence and nonexistence of categorical quotients for algebraic group actions in the categories of algebraic varieties and algebraic prevarieties.
Categorical Quotients for Simplicial Toric Varieties
, 2000
"... We prove a criterion for the existence of a categorical quotient for the action of a subtorus on a simplicial non–degenerate toric variety in the category of Q–factorial algebraic varieties. ..."
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Cited by 1 (1 self)
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We prove a criterion for the existence of a categorical quotient for the action of a subtorus on a simplicial non–degenerate toric variety in the category of Q–factorial algebraic varieties.
FACTORIAL ALGEBRAIC GROUP ACTIONS AND CATEGORICAL QUOTIENTS
, 908
"... Abstract. Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as quotients, we obtain a more general existence resul ..."
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Abstract. Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as quotients, we obtain a more general existence
A CATEGORICAL QUOTIENT IN THE CATEGORY OF DENSE CONSTRUCTIBLE SUBSETS
, 2009
"... A. A’CampoNeuen and J. Hausen gave an example of an algebraic torus action on an open subset of the affine four space that admits no quotient in the category of algebraic varieties. We show that this example admits a quotient in the category of dense constructible subsets and thereby answer a quest ..."
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A. A’CampoNeuen and J. Hausen gave an example of an algebraic torus action on an open subset of the affine four space that admits no quotient in the category of algebraic varieties. We show that this example admits a quotient in the category of dense constructible subsets and thereby answer a
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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be constructed as the quotient (C n+1 −{0})/C ∗. In §2, we will see that there is a similar construction for any toric variety X. In this case, the algebraic group G = HomZ(An−1(X), C ∗ ) acts on an affine space C ∆(1) such that the categorical quotient (C ∆(1) − Z)/G exists and is isomorphic to X
Smooth Surjective Toric Quotients are Categorical
, 1999
"... We prove a criterion for the existence of a categorical quotient for the action of a subtorus on a smooth nondegenerate toric variety in the category of smooth algebraic varieties. ..."
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We prove a criterion for the existence of a categorical quotient for the action of a subtorus on a smooth nondegenerate toric variety in the category of smooth algebraic varieties.
QUOTIENTS OF GROUPOIDS Contents
"... 2. Conventions and notation 1 3. Invariant morphisms 1 4. Categorical quotients 2 ..."
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2. Conventions and notation 1 3. Invariant morphisms 1 4. Categorical quotients 2
Weakly Proper Toric Quotients
, 2004
"... We consider subtorus actions on complex toric varieties. A natural candidate for a categorical quotient of such an action is the so–called toric quotient, a universal object constructed in the toric category. We prove that if the toric quotient is weakly proper and if in addition the quotient variet ..."
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We consider subtorus actions on complex toric varieties. A natural candidate for a categorical quotient of such an action is the so–called toric quotient, a universal object constructed in the toric category. We prove that if the toric quotient is weakly proper and if in addition the quotient
Quotients of Toric Varieties with Curve Lifting Property
, 2000
"... We consider subtorus actions on toric varieties. A natural candidate for a categorical quotient of such an action is the so–called toric quotient, a universal object constructed in the toric category. We prove that if the toric quotient satisfies a certain curve lifting property and if in addition t ..."
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Cited by 2 (0 self)
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We consider subtorus actions on toric varieties. A natural candidate for a categorical quotient of such an action is the so–called toric quotient, a universal object constructed in the toric category. We prove that if the toric quotient satisfies a certain curve lifting property and if in addition
Results 1  10
of
99