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478
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
Branes and Toric Geometry
, 1997
"... We show that toric geometry can be used rather effectively to translate a brane configuration to geometry. Roughly speaking the skeletons of toric space are identified with the brane configurations. The cases where the local geometry involves hypersurfaces in toric varieties (such as P2 blown up at ..."
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Cited by 78 (12 self)
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We show that toric geometry can be used rather effectively to translate a brane configuration to geometry. Roughly speaking the skeletons of toric space are identified with the brane configurations. The cases where the local geometry involves hypersurfaces in toric varieties (such as P2 blown up
Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
, 1995
"... We use the gauged linear sigma model introduced by Witten to calculate instanton expansions for correlation functions in topological sigma models with target space a toric variety V or a Calabi–Yau hypersurface M ⊂ V. In the linear model the instanton moduli spaces are relatively simple objects and ..."
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Cited by 162 (14 self)
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We use the gauged linear sigma model introduced by Witten to calculate instanton expansions for correlation functions in topological sigma models with target space a toric variety V or a Calabi–Yau hypersurface M ⊂ V. In the linear model the instanton moduli spaces are relatively simple objects
On the log discrepancies in toric Mori contractions
"... Abstract. It was conjectured by McKernan and Shokurov that for all Mori contractions from X to Y of given dimensions, for any positive ε there is a positive δ such that if X is εlog terminal, then Y is δlog terminal. We prove this conjecture in the toric case and discuss the dependence of δ on ε, ..."
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Cited by 1 (0 self)
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Abstract. It was conjectured by McKernan and Shokurov that for all Mori contractions from X to Y of given dimensions, for any positive ε there is a positive δ such that if X is εlog terminal, then Y is δlog terminal. We prove this conjecture in the toric case and discuss the dependence of δ on ε
SYZYGIES OF PROJECTIVE TORIC VARIETIES
, 2003
"... If L is an ample line bundle on a toric variety X, then L ⊗d embeds X as a projectively normal variety in P r: = P ( H 0 (X, L ⊗d) ) when d ≥ dim X − 1. In this paper, we prove that the homogeneous ideal I of X in P r is generated by quadrics when d ≥ dim X and the first (p −1) syzygies of I are l ..."
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Cited by 2 (0 self)
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are linear when d ≥ dimX −1+p. Assuming that X is Gorenstein, we also establish similar results for the adjoint series KX ⊗ L ⊗d, solving (the toric case of) a problem posed by Ein and Lazarsfeld.
The toric cobordisms
, 2008
"... A smooth closed 3manifold M fibered by tori T 2 is characterized by an element ϕ ∈ GL(2, Z). We show that M is the boundary of a 4manifold fibered by tori over a surface such that the bundle structure on M is the restriction of the bundle structure on the 4manifold if and only if ϕ is from the co ..."
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the commutator subgroup (GL(2, Z)) ′. The notions of oriented and unoriented cobordisms in the class of closed 3manifolds fibered by tori are introduced. It turns out that in this case the cobordisms form a group, namely Z12 in the oriented case and Z2 ⊕ Z2 in the unoriented one. When the surface on the base
Toric genera
, 2009
"... Our primary aim is to develop a theory of equivariant genera for stably complex manifolds equipped with compatible actions of a torus T k. In the case of omnioriented quasitoric manifolds, we present computations that depend only on their defining combinatorial data; these draw inspiration from ana ..."
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Our primary aim is to develop a theory of equivariant genera for stably complex manifolds equipped with compatible actions of a torus T k. In the case of omnioriented quasitoric manifolds, we present computations that depend only on their defining combinatorial data; these draw inspiration from
Toric dynamical systems
 J. Symbolic Comput
"... Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems and all detailed balancing systems. One feature is that the ..."
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Cited by 49 (10 self)
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Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems and all detailed balancing systems. One feature
Intersection theory on toric varieties
, 1994
"... The operational Chow cohomology classes of a complete toric variety are identified with certain functions, called Minkowski weights, on the corresponding fan. The natural product of Chow cohomology classes makes the Minkowski weights into a commutative ring; the product is computed by a displacement ..."
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Cited by 18 (0 self)
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The operational Chow cohomology classes of a complete toric variety are identified with certain functions, called Minkowski weights, on the corresponding fan. The natural product of Chow cohomology classes makes the Minkowski weights into a commutative ring; the product is computed by a
Results 1  10
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478