Motivic and quantum invariance under stratified Mukai flops (2008)
For stratified Mukai flops of type $A_{n,k}, D_{2k+1}$ and $E_{6,I}$, it is shown the fiber product induces isomorphisms on Chow motives. In contrast to (standard) Mukai flops, the cup product is...
Motivic and quantum invariance under stratified Mukai flops (2008)
For stratified Mukai flops of type $A_{n,k}, D_{2k+1}$ and $E_{6,I}$, it is shown the fiber product induces isomorphisms between Chow motives, cohomology rings and full Gromov-Witten theory.
Motivic and quantum invariance under stratified Mukai flops (2008)
For stratified Mukai flops of type $A_{n,k}, D_{2k+1}$ and $E_{6,I}$, it is shown the fiber product induces isomorphisms between Chow motives, cohomology rings and full Gromov-Witten theory.
Motivic and quantum invariance under stratified Mukai flops (2008)
For stratified Mukai flops of type $A_{n,k}, D_{2k+1}$ and $E_{6,I}$, it is shown the fiber product induces isomorphisms on Chow motives. In contrast to (standard) Mukai flops, the cup product is...
Motivic and quantum invariance under stratified Mukai flops (2008)
For stratified Mukai flops of type $A_{n,k}, D_{2k+1}$ and $E_{6,I}$, it is shown the fiber product induces isomorphisms on Chow motives. In contrast to (standard) Mukai flops, the cup product is...
Elliptic functions, Green functions and the mean field equations on tori (2006)
Lin, Chang-Shou, Wang, Chin-Lung
We show that the Green functions on flat tori can have either 3 or 5 critical points only. There does not seemto be any directmethod to attack this problem. Instead, we have to employ sophisticated...
Flops, motives and invariance of quantum rings (2006)
For ordinary flops, the correspondence defined by the graph closure is shown to give equivalence of Chow motives and to preserve the Poincar\'e pairing. In the case of simple ordinary flops, this...
Quasi-Hodge Metrics and Canonical Singularities (2002)
We study one parameter degenerations of complex projective manifolds by introducing certain type of Hodge metrics coming from the pluricanonical forms. We show that degenerations with at most...
K-equivalence in Birational Geometry (2002)
We give a survey of the background and recent development on the $K$-equivalence relation among birational manifolds. After a brief historical sketch of birational geometry, we define the $K$-partial...
Cohomology Theory in Birational Geometry (2002)
This is a continuation of [9], where it was shown that K-equivalent complex projective manifolds have the same Betti numbers by using the theory of p-adic integrals and Deligne's solution to the Weil...
K-equivalence in Birational Geometry and Characterizations of Complex Elliptic Genera (2001)
We show that for smooth complex projective varieties the most general combinations of chern numbers that are invariant under the K-equivalence relation consist of the complex elliptic genera....
On the Topology of Birational Minimal Models (1998)
We show that birational smooth complex projective varieties with numerically effective canonical bundles along the exceptional loci have the same Betti numbers. In particular, birational smooth...
Topology of birational manifolds and applications to degenerations / (1998)
Thesis (Ph. D.)--Harvard University, 1998.