No abstract uploaded!

We develop a local cohomology theory for FI^m-modules, and show that it in many ways mimics the classical theory for multi-graded modules over a polynomial ring. In particular, we define an invariant of FI^m-modules using this local cohomology theory which closely resembles an invariant of multi-graded modules over Cox rings defined by Maclagan and Smith. It is then shown that this invariant behaves almost identically to the invariant of Maclagan and Smith.

No abstract uploaded!

We prove the Bershadsky-Cecotti-Ooguri-Vafa's conjecture for all genus Gromov-Witten potentials of the quintic threefolds, by identifying the Feynman graph sum with the $\nmsp$ stable graph sum via an R-matrix action. The Yamaguchi-Yau functional equations and the formulas of $F_1,F_2$, are direct consequences of the BCOV Feynman sum rule.

No abstract uploaded!