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Stringy Hodge numbers of threefolds
, 2006
"... Batyrev has defined the stringy Efunction for complex varieties with at most log terminal singularities. It is a rational function in two variables if the singularities are Gorenstein. Furthermore, if the variety is projective and its stringy Efunction is a polynomial, Batyrev defined its stringy ..."
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Hodge numbers essentially as the coefficients of this Efunction, generalizing the usual notion of Hodge numbers of a nonsingular projective variety. He conjectured that they are nonnegative. We prove this in the threefold case in full generality, and also for fourfolds and fivefolds with at most
DEFECT AND HODGE NUMBERS OF HYPERSURFACES
, 2007
"... We define defect for hypersurfaces with ADE singularities in complex projective normal CohenMacaulay fourfolds having some vanishing properties of Botttype and prove formulae for Hodge numbers of big resolutions of such hypersurfaces. We compute Hodge numbers of CalabiYau manifolds obtained as ..."
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Cited by 3 (1 self)
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We define defect for hypersurfaces with ADE singularities in complex projective normal CohenMacaulay fourfolds having some vanishing properties of Botttype and prove formulae for Hodge numbers of big resolutions of such hypersurfaces. We compute Hodge numbers of CalabiYau manifolds obtained
Eigenvalues of Frobenius and Hodge numbers
 Pure Appl. Math. Q
"... We study the connection between Hodge purity of the cohomology of algebraic varieties over fields of different characteristics. Specifically, we study varieties over number fields, whose cohomology in some fixed degree 2i consists entirely of Hodge classes, that is, whose Hodge cohomology in degree ..."
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Cited by 6 (2 self)
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We study the connection between Hodge purity of the cohomology of algebraic varieties over fields of different characteristics. Specifically, we study varieties over number fields, whose cohomology in some fixed degree 2i consists entirely of Hodge classes, that is, whose Hodge cohomology in degree
The Jumping Phenomenon of Hodge Numbers
, 2008
"... Let X be a compact complex manifold, consider a small deformation φ: X → B of X, the dimension of the Dolbeault cohomology groups Hq (Xt,Ω p) may vary under this defromation. This paper ..."
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Let X be a compact complex manifold, consider a small deformation φ: X → B of X, the dimension of the Dolbeault cohomology groups Hq (Xt,Ω p) may vary under this defromation. This paper
Stringy Hodge Numbers and Virasoro Algebra
"... Let X be an arbitrary smooth ndimensional projective variety. It was discovered by Libgober and Wood that the product of the Chern classes c1(X)cn−1(X) depends only on the Hodge numbers of X. This result has been used by Eguchi, Jinzenji and Xiong in their approach to the quantum cohomology of X vi ..."
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Cited by 6 (1 self)
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Let X be an arbitrary smooth ndimensional projective variety. It was discovered by Libgober and Wood that the product of the Chern classes c1(X)cn−1(X) depends only on the Hodge numbers of X. This result has been used by Eguchi, Jinzenji and Xiong in their approach to the quantum cohomology of X
STRINGY HODGE NUMBERS AND PADIC HODGE THEORY
, 2002
"... The aim of this paper is to give an application of padic Hodge theory to stringy Hodge numbers introduced by V. Batyrev for a mathematical formulation of mirror symmetry. Since the stringy Hodge numbers of an algebraic variety are defined by choosing a resolution of singularities, the welldefine ..."
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Cited by 7 (1 self)
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The aim of this paper is to give an application of padic Hodge theory to stringy Hodge numbers introduced by V. Batyrev for a mathematical formulation of mirror symmetry. Since the stringy Hodge numbers of an algebraic variety are defined by choosing a resolution of singularities, the well
Stringy Hodge numbers of varieties with Gorenstein canonical singularities
 Proc. Taniguchi Symposium 1997, In ‘Integrable Systems and Algebraic Geometry, Kobe/Kyoto 1997’, World
, 1999
"... We introduce the notion of stringy Efunction for an arbitrary normal irreducible algebraic variety X with at worst logterminal singularities. We prove some basic properties of stringy Efunctions and compute them explicitly for arbitrary QGorenstein toric varieties. Using stringy Efunctions, we ..."
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Cited by 98 (5 self)
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propose a general method to define stringy Hodge numbers for projective algebraic varieties with at worst Gorenstein canonical singularities. This allows us to formulate the topological mirror duality test for arbitrary CalabiYau varieties with canonical singularities. In Appendix we explain non
Orbifold Hodge numbers of the wreath product orbifolds
 J. Geom. Phys
"... Abstract. We prove that the wreath product orbifolds studied earlier by the first author provide a large class of higher dimensional examples of orbifolds whose orbifold Hodge numbers coincide with the ordinary ones of suitable resolutions of singularities. We also make explicit conjectures on ellip ..."
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Cited by 14 (3 self)
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Abstract. We prove that the wreath product orbifolds studied earlier by the first author provide a large class of higher dimensional examples of orbifolds whose orbifold Hodge numbers coincide with the ordinary ones of suitable resolutions of singularities. We also make explicit conjectures
(b) Reflexive Polyhedra And Hodge Numbers
, 1996
"... We present a systematic way of generating Ftheory models dual to nonperturbative vacua (i.e., vacua with extra tensor multiplets) of heterotic E8×E8 strings compactified on K3, using hypersurfaces in toric varieties. In all cases, the CalabiYau is an elliptic fibration over a blow up of the Hirzeb ..."
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We present a systematic way of generating Ftheory models dual to nonperturbative vacua (i.e., vacua with extra tensor multiplets) of heterotic E8×E8 strings compactified on K3, using hypersurfaces in toric varieties. In all cases, the CalabiYau is an elliptic fibration over a blow up of the Hirzebruch surface IFn. We find that in most cases the fan of the base of the elliptic fibration is visible in the dual polyhedron of the CalabiYau, and that the extra tensor multiplets are represented as points corresponding to the blowups of the IFn.
Results 1  10
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