A strictly decreasing invariant for resolution of singularities in dimension two

Abstract

We construct a local invariant for resolution of singularities of 2-dimensional excellent Noetherian schemes with boundary. We prove that the invariant strictly decreases at every step of the algorithm of Cossart, Jannsen and Saito.

arXiv comment41 pages, improved exposition, clarified minor details, added section of the termination of the CJS algorithm