On taut singularities in arbitrary characteristics

Abstract

Over $\C$, Henry Laufer classified all taut surface singularities. We adapt and extent his transcendental methods to positive characteristic. With this we show that if a normal surface singularity is taut over $\C$, then the normal surface singularities with isomorphic dual graph over algebraically closed fields of characteristic exponent $p>1$ are taut for all but finitely many $p$. We conjecture that this is actually "if and only if".