20 citations · 30 across the 4 of their papers we have counts for
6 papers
Integral affine structures on spheres III: complete intersections
Christian Haase, Ilia Zharkov
We extend our model for affine structures on toric Calabi-Yau hypersurfaces math.AG/0205321 to the case of complete intersections.
Limiting behavior of local Calabi-Yau metrics
Ilia Zharkov
We use a generalization of the Gibbons-Hawking ansatz to study the behavior of certain non-compact Calabi-Yau manifolds in the large complex structure limit. This analysis provides…
Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces II
Christian Haase, Ilia Zharkov
This paper is a continuation of our paper math.AG/0205321 where we have built a combinatorial model for the torus fibrations of Calabi-Yau toric hypersurfaces. This part addresses…
Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces I
Christian Haase, Ilia Zharkov
We describe in purely combinatorial terms dual pairs of integral affine structures on spheres which come from the conjectural metric collapse of mirror families of Calabi-Yau toric…
Theta-functions for indefinite polarizations
Ilia Zharkov
We propose a generalization of the classical theta function to higher cohomology of the polarization line bundle on a family of complex tori with positive index. The constructed co…
Torus Fibrations of Calabi-Yau Hypersurfaces in Toric Varieties and Mirror Symmetry
Ilia Zharkov
We consider regular Calabi-Yau hypersurfaces in -dimensional smooth toric varieties. On such a hypersurface in the neighborhood of the large complex structure limit point we con…