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Geometry of CalabiYau manifolds
"... CalabiYau manifolds are certain higher dimensional generalisations of Riemann surfaces of genus one. Calabi Yau manifolds of dimension two form the wellstudied class of K3surfaces. It turns out that there exist a myriad of topologically different CalabiYau threefolds. However, their classificati ..."
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CalabiYau manifolds are certain higher dimensional generalisations of Riemann surfaces of genus one. Calabi Yau manifolds of dimension two form the wellstudied class of K3surfaces. It turns out that there exist a myriad of topologically different CalabiYau threefolds. However
Convergence of CalabiYau manifolds
, 2009
"... In this paper, we study the convergence of CalabiYau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of CalabiYau manifolds. ..."
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Cited by 13 (3 self)
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In this paper, we study the convergence of CalabiYau manifolds under Kähler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of CalabiYau manifolds.
Generalized CalabiYau manifolds
 Q. J. Math
"... A geometrical structure on evendimensional manifolds is defined which generalizes the notion of a CalabiYau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2forms. In the special case o ..."
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Cited by 326 (3 self)
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A geometrical structure on evendimensional manifolds is defined which generalizes the notion of a CalabiYau manifold and also a symplectic manifold. Such structures are of either odd or even type and can be transformed by the action of both diffeomorphisms and closed 2forms. In the special case
Calabi–Yau manifolds for dummies
, 2008
"... In the text below we try to introduce the concept of a Calabi–Yau manifold. We start by defining vector bundles and complex manifolds, then introduce Kähler manifolds, review the most rudimentary concepts of Chern classes and then define Calabi–Yau manifolds. We also comment on the importance of Cal ..."
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In the text below we try to introduce the concept of a Calabi–Yau manifold. We start by defining vector bundles and complex manifolds, then introduce Kähler manifolds, review the most rudimentary concepts of Chern classes and then define Calabi–Yau manifolds. We also comment on the importance
ON SPECIAL GENERALIZED CALABIYAU MANIFOLDS
, 2007
"... Abstract. We construct examples of special generalized CalabiYau manifolds on compact quotients of solvable Lie groups. We prove that the CalabiYau structures are not rigid in the class of special generalized CalabiYau structures. Moreover, we provide an example of a compact 6dimensional special ..."
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Abstract. We construct examples of special generalized CalabiYau manifolds on compact quotients of solvable Lie groups. We prove that the CalabiYau structures are not rigid in the class of special generalized CalabiYau structures. Moreover, we provide an example of a compact 6dimensional
ON THE MODULI SPACE OF CALABIYAU MANIFOLDS
"... Let X be a simply connected compact Kähler manifold with zero first Chern class, and let L be an ample line bundle over X. The pair (X,L) is called a polarized CalabiYau manifold. By a theorem of Mumford, the moduli space of the pair (X,L) (CY moduli) exists and ..."
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Let X be a simply connected compact Kähler manifold with zero first Chern class, and let L be an ample line bundle over X. The pair (X,L) is called a polarized CalabiYau manifold. By a theorem of Mumford, the moduli space of the pair (X,L) (CY moduli) exists and
The Rigidity of Families of Polarized CalabiYau Manifolds
, 2004
"... In this paper,we study the Shafarevich conjecture for moduli space of polarized CalabiYau manifolds and obtain some results on the rigidity of families of CalabiYau manifolds. We use variation of Hodge structure and Higgs bundle to establish a criterion for rigidity and apply it to show some impor ..."
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In this paper,we study the Shafarevich conjecture for moduli space of polarized CalabiYau manifolds and obtain some results on the rigidity of families of CalabiYau manifolds. We use variation of Hodge structure and Higgs bundle to establish a criterion for rigidity and apply it to show some
CalabiYau Manifolds with BFields
"... Calabi*Yau manifolds with B*o/elds F. Witt * February 29, 2008 Abstract In recent work N. Hitchin introduced the concept of igeneralised geometryj. The key feature of generalised structures is that that they can be acted on by both dioeeomorphisms and 2*forms, the so*called B*o/elds. In this lecture ..."
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Cited by 3 (0 self)
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Calabi*Yau manifolds with B*o/elds F. Witt * February 29, 2008 Abstract In recent work N. Hitchin introduced the concept of igeneralised geometryj. The key feature of generalised structures is that that they can be acted on by both dioeeomorphisms and 2*forms, the so*called B
NonCommutative CalabiYau Manifolds
, 2008
"... We discuss aspects of the algebraic geometry of compact noncommutative CalabiYau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact CalabiYau algebra. We consider two examples: a toroidal orbifold T 6 /Z2 ×Z2, and an orb ..."
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Cited by 1 (0 self)
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We discuss aspects of the algebraic geometry of compact noncommutative CalabiYau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact CalabiYau algebra. We consider two examples: a toroidal orbifold T 6 /Z2 ×Z2
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