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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 Coordinates
 Visual Comput 10:176–187
, 1994
"... this paper we have offered a unified view of homogeneous coordinates within a Computer Graphics context. First, a brief historical review revealed that, as the understanding of perspective and projections increased, new coordinate systems were developed to represent the underlying spaces; one of the ..."
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Cited by 12 (0 self)
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this paper we have offered a unified view of homogeneous coordinates within a Computer Graphics context. First, a brief historical review revealed that, as the understanding of perspective and projections increased, new coordinate systems were developed to represent the underlying spaces; one
Homogeneous Coordinates for Algebraic Varieties
, 2002
"... We associate to every divisorial (e.g. smooth) variety X with only constant invertible global functions and finitely generated Picard group a Pic(X)graded homogeneous coordinate ring. This generalizes the usual homogeneous coordinate ring of the projective space and constructions of Cox and Kajiwar ..."
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Cited by 24 (7 self)
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We associate to every divisorial (e.g. smooth) variety X with only constant invertible global functions and finitely generated Picard group a Pic(X)graded homogeneous coordinate ring. This generalizes the usual homogeneous coordinate ring of the projective space and constructions of Cox
Clipping Using Homogeneous Coordinates
 Proceedings of SIGGRAPH ’78
, 1978
"... Clipping is the process of determining how much of a given line segment lies within the boundaries of the display screen. Homogeneous coordinates are a convenient mathematical device for representing and transforming objects. The space represented by homogeneous coordinates is not, however, a simple ..."
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Cited by 10 (0 self)
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Clipping is the process of determining how much of a given line segment lies within the boundaries of the display screen. Homogeneous coordinates are a convenient mathematical device for representing and transforming objects. The space represented by homogeneous coordinates is not, however, a
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.
Image Mosaics Base on Homogeneous Coordinates
"... The need to combine pictures into panoramic mosaics has existed since the beginning of photography, as the camera's field of view is always smaller than the human field of view. Photo mosaicing, a technique to paste together several pictures to create a panoramic mosaic, gives us a more complet ..."
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complete view of the scene. In this paper, an image mosaic approach is proposed. Homogeneous coordinates are used to represent points. The overlapped points for each RGB channel are interpolated to generate mosaics after projecting the points from different images to the reference image. Experiments
Education Barycentric coordinates computation in homogeneous coordinates
, 2007
"... Homogeneous coordinates are often used in computer graphics and computer vision applications especially for the representation of geometric transformations. The homogeneous coordinates enable us to represent translation, rotation, scaling and projection operations in a unique way and handle them pro ..."
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Cited by 4 (3 self)
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Homogeneous coordinates are often used in computer graphics and computer vision applications especially for the representation of geometric transformations. The homogeneous coordinates enable us to represent translation, rotation, scaling and projection operations in a unique way and handle them
Homogeneous coordinates and quotient presentations for toric varieties
 MATH. NACHR
, 2000
"... Generalizing cones over projective toric varieties, we present arbitrary toric varieties as quotients of quasiaffine toric varieties. Such quotient presentations correspond to groups of Weil divisors generating the topology. Groups comprising Cartier divisors define free quotients, whereas QCartie ..."
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Cited by 10 (3 self)
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Cartier divisors define geometric quotients. Each quotient presentation yields homogeneous coordinates. Using homogeneous coordinates, we express quasicoherent sheaves in terms of multigraded modules and describe the set of morphisms into a toric variety.
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 group G0(RG) of all finitely generated RGmodules lie in a finitely generated subgroup. Under various hypotheses, we show that there is a finite set of indecomposable RGmodules such that each H 0 (X, F ⊗ L n) is a direct sum of these indecomposables, with multiplicites given by generalized Hilbert polynomials for n>> 0. 1.
Results 1  10
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1,528