Stable Cohomology of Discriminant Complements for an algebraic curve

Abstract

In this paper we show that in a stable range the cohomology of the space of regular algebraic sections of a line bundle $\mathcal{L}$on a curve $X$ is isomorphic to the cohomology of the space of regular $C^{\infty }$sections of the same line bundle.

arXiv commentUpdate(11/14/2022) Fixed several typos, clarified definition of U_n^{alg}, added more details and clarifications in several sections. Both statement and proof of main theorem remain unchanged