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Cohomological dimension of certain algebraic varieties
 PROC. AMER. MATH. SOC
, 2002
"... Let a be an ideal of a commutative Noetherian ring R. For finitely generated Rmodules M and N with SuppN ⊆ SuppM, it is shown that cd(a, N) ≤ cd(a,M). Let N be a finitely generated module over a local ring (R,m) such that Min ..."
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Cited by 25 (6 self)
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Let a be an ideal of a commutative Noetherian ring R. For finitely generated Rmodules M and N with SuppN ⊆ SuppM, it is shown that cd(a, N) ≤ cd(a,M). Let N be a finitely generated module over a local ring (R,m) such that Min
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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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
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 523 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
Dual polyhedra and mirror symmetry for Calabi–Yau hypersurfaces in toric varieties
 J. Alg. Geom
, 1994
"... We consider families F(∆) consisting of complex (n − 1)dimensional projective algebraic compactifications of ∆regular affine hypersurfaces Zf defined by Laurent polynomials f with a fixed ndimensional Newton polyhedron ∆ in ndimensional algebraic torus T = (C ∗ ) n. If the family F(∆) defined by ..."
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Cited by 467 (20 self)
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We consider families F(∆) consisting of complex (n − 1)dimensional projective algebraic compactifications of ∆regular affine hypersurfaces Zf defined by Laurent polynomials f with a fixed ndimensional Newton polyhedron ∆ in ndimensional algebraic torus T = (C ∗ ) n. If the family F(∆) defined
Comprehending Monads
 Mathematical Structures in Computer Science
, 1992
"... Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised t ..."
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Cited by 521 (18 self)
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Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised
Automating the Design of Graphical Presentations of Relational Information
 ACM Transactions on Graphics
, 1986
"... The goal of the research described in this paper is to develop an applicationindependent presentation tool that automatically designs effective graphical presentations (such as bar charts, scatter plots, and connected graphs) of relational information. Two problems are raised by this goal: The codi ..."
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Cited by 559 (9 self)
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exploits the capabilities of the output medium and the human visual system. A wide variety of designs can be systematically generated by using a composition algebra that composes a small set of primitive graphical languages. Artificial intelligence techniques are used to implement a prototype presentation
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 506 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k
Alternatingtime Temporal Logic
 Journal of the ACM
, 1997
"... Temporal logic comes in two varieties: lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general var ..."
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Cited by 620 (53 self)
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Temporal logic comes in two varieties: lineartime temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branchingtime temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general
PVM: A Framework for Parallel Distributed Computing
 Concurrency: Practice and Experience
, 1990
"... The PVM system is a programming environment for the development and execution of large concurrent or parallel applications that consist of many interacting, but relatively independent, components. It is intended to operate on a collection of heterogeneous computing elements interconnected by one or ..."
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Cited by 788 (27 self)
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components, is portable to a variety of architectures, and supports certain forms of error dete...
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