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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
The geometry of algorithms with orthogonality constraints
 SIAM J. MATRIX ANAL. APPL
, 1998
"... In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal proces ..."
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Cited by 640 (1 self)
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In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 474 (3 self)
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Field Theories are defined, and it is proved that tree level theories are determined by their correlation functions. Application to counting rational curves on del Pezzo surfaces and projective spaces are given. Let V be a projective algebraic manifold. Methods of quantum field theory recently led to a
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
KSTABILITY OF CONSTANT SCALAR CURVATURE POLARIZATION
, 2008
"... In this paper, we shall show that a polarized algebraic manifold is Kstable if the polarization class admits a Kähler metric of constant scalar curvature. This generalizes the results of ChenTian [1], Donaldson [4] and Stoppa [20]. ..."
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Cited by 25 (1 self)
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In this paper, we shall show that a polarized algebraic manifold is Kstable if the polarization class admits a Kähler metric of constant scalar curvature. This generalizes the results of ChenTian [1], Donaldson [4] and Stoppa [20].
Gravity coupled with matter and the foundation of non commutative geometry
, 1996
"... We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D i ..."
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Cited by 343 (17 self)
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We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element ds. Its unitary representations correspond to Riemannian metrics and Spin structure while ds is the Dirac propagator ds = ×— × = D −1 where D
AN ENERGYTHEORETIC APPROACH TO THE HITCHINKOBAYASHI CORRESPONDENCE FOR MANIFOLDS, II
, 2004
"... Recently, Donaldson proved asymptotic stability for a polarized algebraic manifold M with polarization class admitting a Kähler metric of constant scalar curvature, essentially when the linear algebraic part H of Aut 0 (M) is semisimple. The purpose of this paper is to give a generalization of Donal ..."
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Cited by 50 (6 self)
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Recently, Donaldson proved asymptotic stability for a polarized algebraic manifold M with polarization class admitting a Kähler metric of constant scalar curvature, essentially when the linear algebraic part H of Aut 0 (M) is semisimple. The purpose of this paper is to give a generalization
A path integral approach to the Kontsevich quantization formula
, 1999
"... We give a quantum field theory interpretation of Kontsevich’s deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory. Its Batalin–Vilkovisky quantization yields a supercon ..."
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Cited by 306 (21 self)
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We give a quantum field theory interpretation of Kontsevich’s deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory. Its Batalin–Vilkovisky quantization yields a
On the 'Piano Movers' Problem II. General Techniques for Computing Topological Properties of Real Algebraic Manifolds
, 1982
"... This paper continues the discussion, begun in [SS], of the following problem, which arises in robotics: Given a collection of bodies B, which may be hinged, i.e. may allow internal motion around various joints, and given a region bounded by a collection of polyhedral or other simple walls, decide ..."
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Cited by 228 (9 self)
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of an arbitrary real algebraic variety. Various algorithmic issues concerning computations with algebraic numbers, which are required in the algorithms presented in this paper, are also reviewed.
Results 1  10
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