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3,993
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
HOMOGENEOUS COORDINATE RING FOR X
, 2010
"... Abstract. We compute the Grothendieck and Picard groups of a smooth toric DM stack by using a suitable category of graded modules over a polynomial ring. The polynomial ring with a suitable grading and suitable irrelevant ideal functions is a homogeneous coordinate ring for the stack. ..."
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Abstract. We compute the Grothendieck and Picard groups of a smooth toric DM stack by using a suitable category of graded modules over a polynomial ring. The polynomial ring with a suitable grading and suitable irrelevant ideal functions is a homogeneous coordinate ring for the stack.
Galois structure of homogeneous coordinate rings
 Trans. Amer. Math. Soc
"... Abstract. Suppose G is a finite group acting on a projective scheme X over a commutative Noetherian ring R. We study the RGmodules H 0 (X, F ⊗ L n) when n ≥ 0, and F and L are coherent Gsheaves on X such that L is an ample line bundle. We show that the classes of these modules in the Grothendieck ..."
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Cited by 2 (0 self)
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Abstract. Suppose G is a finite group acting on a projective scheme X over a commutative Noetherian ring R. We study the RGmodules H 0 (X, F ⊗ L n) when n ≥ 0, and F and L are coherent Gsheaves on X such that L is an ample line bundle. We show that the classes of these modules in the Grothendieck
THE DIXMIERMOEGLIN EQUIVALENCE FOR TWISTED HOMOGENEOUS COORDINATE RINGS
, 2008
"... Given a projective scheme X over a field k, an automorphism σ: X → X, and a σample invertible sheaf L, one may form the twisted homogeneous coordinate ring B = B(X, L, σ), one of the most fundamental constructions in noncommutative projective algebraic geometry. We study the primitive spectrum of ..."
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Cited by 8 (6 self)
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Given a projective scheme X over a field k, an automorphism σ: X → X, and a σample invertible sheaf L, one may form the twisted homogeneous coordinate ring B = B(X, L, σ), one of the most fundamental constructions in noncommutative projective algebraic geometry. We study the primitive spectrum
Some homogeneous coordinate rings that are Koszul algebras
, 1995
"... Abstract. Using reduction to positive characteristic and the method of Frobenius splitting of diagonals, due to Mehta and Ramanathan, it is shown that homogeneous coordinate rings for either proper and smooth toric varieties or Schubert varieties are Koszul algebras. 1.Introduction. All varieties wi ..."
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Cited by 4 (0 self)
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Abstract. Using reduction to positive characteristic and the method of Frobenius splitting of diagonals, due to Mehta and Ramanathan, it is shown that homogeneous coordinate rings for either proper and smooth toric varieties or Schubert varieties are Koszul algebras. 1.Introduction. All varieties
On the Koszul property of the homogeneous coordinate ring of a curve
 J. Algebra
, 1995
"... This paper is devoted to Koszul property of the homogeneous coordinate algebra of a smooth complex algebraic curve in the projective space (the notion of a Koszul algebra is some homological refinement of the notion of a quadratic algebra, for precise definition see next section). It grew out from ..."
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Cited by 10 (1 self)
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This paper is devoted to Koszul property of the homogeneous coordinate algebra of a smooth complex algebraic curve in the projective space (the notion of a Koszul algebra is some homological refinement of the notion of a quadratic algebra, for precise definition see next section). It grew out from
EXTENSIONS OF HOMOGENEOUS COORDINATE RINGS TO A∞ALGEBRAS
, 2003
"... Abstract. We study A∞structures extending the natural algebra structure on the cohomology of ⊕n∈ZL n, where L is a very ample line bundle on a projective ddimensional variety X such that H i (X, L n) = 0 for 0 < i < d and all n ∈ Z. We prove that there exists a unique such nontrivial A∞str ..."
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Cited by 6 (2 self)
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Abstract. We study A∞structures extending the natural algebra structure on the cohomology of ⊕n∈ZL n, where L is a very ample line bundle on a projective ddimensional variety X such that H i (X, L n) = 0 for 0 < i < d and all n ∈ Z. We prove that there exists a unique such nontrivial A∞structure up to a strict A∞isomorphism (i.e., an A∞isomorphism with the identity as the first structure map) and rescaling. In the case when X is a curve we also compute the group of strict A∞automorphisms of this A∞structure. 1.
DEGENERATE SKLYANIN ALGEBRAS AND GENERALIZED TWISTED HOMOGENEOUS COORDINATE RINGS
, 812
"... Abstract. In this work, we introduce the point parameter ring B, a generalized twisted homogeneous coordinate ring associated to a degeneration of the threedimensional Sklyanin algebra. The surprising geometry of these algebras yields an analogue to a result of ArtinTatevan den Bergh, namely that ..."
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Cited by 3 (2 self)
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Abstract. In this work, we introduce the point parameter ring B, a generalized twisted homogeneous coordinate ring associated to a degeneration of the threedimensional Sklyanin algebra. The surprising geometry of these algebras yields an analogue to a result of ArtinTatevan den Bergh, namely
TWISTED HOMOGENEOUS COORDINATE RINGS OF ABELIAN SURFACES VIA MIRROR SYMMETRY
, 2006
"... Abstract. In this paper we study Seidel’s mirror map for abelian and Kummer surfaces. We find that mirror symmetry leads in a very natural way to the classical parametrization of Kummer surfaces in P 3. Moreover, we describe a family of embeddings of a given abelian surface into noncommutative proje ..."
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Cited by 1 (1 self)
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Abstract. In this paper we study Seidel’s mirror map for abelian and Kummer surfaces. We find that mirror symmetry leads in a very natural way to the classical parametrization of Kummer surfaces in P 3. Moreover, we describe a family of embeddings of a given abelian surface into noncommutative projective spaces. 1.
Results 1  10
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3,993