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A new geometric approach to problems in birational geometry
Chen-Yu Chi, Shing-Tung Yau
A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a t…
Morphisms from Azumaya prestable curves with a fundamental module to a projective variety: Topological D-strings as a master object for curves
Si Li, Chien-Hao Liu, Ruifang Song +1
This is a continuation of our study of the foundations of D-branes from the viewpoint of Grothendieck in the region of the related Wilson's theory-space where "branes" are still br…
Balanced metrics on non-Kahler Calabi-Yau threefolds
Jixiang Fu, Jun Li, Shing-Tung Yau
We construct balanced metrics on the family of non-Kähler Calabi-Yau threefolds that are obtained by smoothing after contracting -rational curves on Kähler Calabi-Yau thre…
New Heterotic Non-Kahler Geometries
Melanie Becker, Li-Sheng Tseng, Shing-Tung Yau
New heterotic torsional geometries are constructed as orbifolds of T^2 bundles over K3. The discrete symmetries considered can be freely-acting or have fixed points and/or fixed cu…
Local Heterotic Torsional Models
Ji-Xiang Fu, Li-Sheng Tseng, Shing-Tung Yau
We present a class of smooth supersymmetric heterotic solutions with a non-compact Eguchi-Hanson space. The non-compact geometry is embedded as the base of a six-dimensional non-Ka…
Isometric embeddings into the Minkowski space and new quasi-local mass
Mu-Tao Wang, Shing-Tung Yau
The definition of quasi-local mass for a bounded space-like region in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is exp…