Results 11 to 20 of about 340 (28)

Balanced metrics and noncommutative Kaehler geometry [PDF]

, 2010
In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions on a Kahler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited from the ...
Lukic, Sergio
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Generalized Borcea-Voisin Construction [PDF]

, 2011
C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution.
A. Garbagnati, C. Borcea, C. Borcea, C. Vafa, J. Dillies, J.C. Rohde, Jimmy Dillies, K. Oguiso, L. Dixon, M. Abe, M. Artebani, M. Artebani, R. Donagi, R. Donagi, S. Cynk, S. Kondō, S. Taki, S.-S. Roan, V.V. Batyrev, W. Chen   +19 more
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A cone conjecture for log Calabi-Yau surfaces

Forum of Mathematics, Sigma
We consider log Calabi-Yau surfaces $(Y, D)$ with singular boundary. In each deformation type, there is a distinguished surface $(Y_e,D_e)$ such that the mixed Hodge structure on $H_2(Y \setminus D)$ is split.
Jennifer Li
doaj   +1 more source

A simple remark on a flat projective morphism with a Calabi-Yau fiber

, 2010
If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field, then any smooth connected fiber is also a K3 surface.
C. Schoen, G. Xu, I. Peeva, K. Oguiso, Keiji Oguiso, N. H. Lee, R. Hartshorne, W. P. Barth, W. P. Barth, Y. Kawamata   +9 more
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Deformations of Calabi–Yau varieties with k-liminal singularities

Forum of Mathematics, Sigma
The goal of this paper is to describe certain nonlinear topological obstructions for the existence of first-order smoothings of mildly singular Calabi–Yau varieties of dimension at least $4$ .
Robert Friedman, Radu Laza
doaj   +1 more source

Minimal log discrepancies of hypersurface mirrors

Forum of Mathematics, Sigma
For certain quasismooth Calabi–Yau hypersurfaces in weighted projective space, the Berglund-Hübsch-Krawitz (BHK) mirror symmetry construction gives a concrete description of the mirror.
Louis Esser
doaj   +1 more source

Nef cones of fiber products and an application to the cone conjecture

Forum of Mathematics, Sigma
We prove a decomposition theorem for the nef cone of smooth fiber products over curves, subject to the necessary condition that their Néron–Severi space decomposes.
Cécile Gachet, Hsueh-Yung Lin, Long Wang   +2 more
doaj   +1 more source

Smoothing, scattering and a conjecture of Fukaya

Forum of Mathematics, Pi
In 2002, Fukaya [19] proposed a remarkable explanation of mirror symmetry detailing the Strominger–Yau–Zaslow (SYZ) conjecture [47] by introducing two correspondences: one between the theory of pseudo-holomorphic curves on a Calabi–Yau manifold ...
Kwokwai Chan, Naichung Conan Leung, Ziming Nikolas Ma   +2 more
doaj   +1 more source

Conifold Transitions for Complete Intersection Calabi-Yau 3-folds in Products of Projective Spaces

, 2012
We prove that a generic complete intersection Calabi-Yau 3-fold defined by sections of ample line bundles on a product of projective spaces admits a conifold transition to a connected sum of S^{3} \times S^{3}.
Xu, Jinxing
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On the birationality of the adjunction mapping of projective varieties [PDF]

, 2011
Let $X$ be a smooth projective $n$-fold such that $q(X)=0$ and $L$ a globally generated, big line bundle on $X$ such that $h^0(K_X+(n-2)L) >0$. We give necessary and sufficient conditions for the adjoint systems $|K_X+kL|$ to be birational for $k \geq n ...
Knutsen, Andreas Leopold
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