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Recent Development on the Geometry of the Teichmuller and Moduli Spaces of Riemann Surfaces and Polarized Calabi-Yau Manifolds
Kefeng Liu, Xiaofeng Sun, Shing-Tung Yau
We survey our recent new results on the geometry of Teichmuller and moduli spaces of Riemann surfaces and Calabi-Yau manifolds.
Global Torelli Theorem for Teichmuller Spaces of Polarized Calabi-Yau manifolds
Kefeng Liu, Andrey Todorov, Xiaofeng Sun +1
The result of this paper is proved in arXiv:1112.1163
Picard-Fuchs Equations for Relative Periods and Abel-Jacobi Map for Calabi-Yau Hypersurfaces
Si Li, Bong H. Lian, Shing-Tung Yau
We study the variation of relative cohomology for a pair consisting of a smooth projective hypersurface and an algebraic subvariety in it. We construct an inhomogeneous Picard-Fuch…
Nontrivial Azumaya noncommutative schemes, morphisms therefrom, and their extension by the sheaf of algebras of differential operators: D-branes in a -field background à la Polchinski-Grothendieck Ansatz
Chien-Hao Liu, Shing-Tung Yau
In this continuation of [L-Y1], [L-L-S-Y], [L-Y2], and [L-Y3] (arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], arXiv:0901.0342 [math.AG], arXiv:0907.0268 [math.AG]), we study…
Cohomology and Hodge Theory on Symplectic Manifolds: I
Li-Sheng Tseng, Shing-Tung Yau
We introduce new finite-dimensional cohomologies on symplectic manifolds. Each exhibits Lefschetz decomposition and contains a unique harmonic representative within each class. Ass…
Azumaya structure on D-branes and deformations and resolutions of a conifold revisited: Klebanov-Strassler-Witten vs. Polchinski-Grothendieck
Chien-Hao Liu, Shing-Tung Yau
In this sequel to [L-Y1], [L-L-S-Y], and [L-Y2] (respectively arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], and arXiv:0901.0342 [math.AG]), we study a D-brane probe on a co…