A twisted ${\bar{\partial }}_f$-Neumann problem and Toeplitz $n$-tuples from singularity theory

Abstract

A twisted ${\bar{\partial }}_f$-Neumann problem associated to a singularity $({\mathcal{O}}_n,f)$ is established. By constructing the connection to the Koszul complex for toeplitz $n$-tuples $(f_1,\cdots ,f_n)$ on Bergman spaces $B^0(D)$, we can solve this ${\bar{\partial }}_f$-Neumann problem. Moreover, we can compute the cohomology of the $L^2$ holomorphic Koszul complex $(B^{\ast }(D),\partial f\wedge )$ explicitly

20 pages

References in corpus (1)

• Schrödinger equations, deformation theory and $t{t}^{\ast }$-geometry