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

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

Given a projective scheme X over a field k, an automorphism σ: X → X, and a σ-ample 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

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

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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

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 d-dimensional 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.

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

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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