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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
Length, Area and Volume Computation in Homogeneous Coordinates
"... Many problems solved in computer graphics, computer vision, visualization etc. require fast and robust computation of an area of a triangle or volume of a tetrahedron. These very often used algorithms are well known and robust if vertices coordinates of triangles or tetrahedrons are given in Euclide ..."
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in Euclidean coordinates. The homogeneous coordinates are often used for the representation of geometric transformations. They enable us to represent translation, rotation, scaling and projection operations in a unique way and handle them properly. Today’s graphics hardware based on GPU offers very high
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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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
Triangle scan conversion using 2d homogeneous coordinates
 In SIGGRAPH/Eurographics Workshop on Graphics Hardware
, 1997
"... We present a new triangle scan conversion algorithm that works entirely in homogeneous coordinates. By using homogeneous coordinates, the algorithm avoids costly clipping tests which make pipelining or hardware implementations of previous scan conversion algorithms difficult. The algorithm handles c ..."
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Cited by 29 (0 self)
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We present a new triangle scan conversion algorithm that works entirely in homogeneous coordinates. By using homogeneous coordinates, the algorithm avoids costly clipping tests which make pipelining or hardware implementations of previous scan conversion algorithms difficult. The algorithm handles
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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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.
INTERSECTION COMPUTATION IN PROJECTIVE SPACE USING HOMOGENEOUS COORDINATES
"... There are many algorithms based on computation of intersection of lines, planes etc. Those algorithms are based on representation in the Euclidean space. Sometimes, very complex mathematical notations are used to express simple mathematical solutions. This paper presents solutions of some selected p ..."
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the intersection of two lines in the case of E2 or the intersection of three planes in the case of E3. Plücker coordinates and principle of duality are used to derive an equation of a parametric line in E3 as an intersection of two planes. This new formulation avoids division operations and increases
HELMER ASLAKSEN RESTRICTED HOMOGENEOUS COORDINATES FOR THE CAYLEY PROJECTIVE PLANE
"... ABSTRACT. I. Porteous has shown that the Cayley projective plane can be coordinatized in a way resembling homogeneous coordinates. We will show how to construct line coordinates in a similar way. As an illustration, we give an explicit example to show that the Cayley projective plane is not Desargue ..."
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ABSTRACT. I. Porteous has shown that the Cayley projective plane can be coordinatized in a way resembling homogeneous coordinates. We will show how to construct line coordinates in a similar way. As an illustration, we give an explicit example to show that the Cayley projective plane
Results 11  20
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1,528