Quasi-Gorenstein (Normal) Finite Covers in Arbitrary Characteristic

Abstract

We show that any complete local (normal) domain admits a module-finite quasi-Gorenstein normal (complete local) domain extension. In the geometric vein, we show that any normal projective variety $X$ over a field admits a finite surjective morphism $Y\to X$ from a normal quasi-Gorenstein projective variety $Y$. Notably, our results resolve the previously open case for residual characteristic two.

Two sections are added. One section establishes the quasi-quasi-Gorenstein finite covers for projective varieties. The other one gives a converse to a result of Paul C. Roberts, with an application. Accepted for publication in the Proceedings of the American Mathematical Society