On taut singularities in arbitrary characteristics

TL;DR

This paper extends the classification of taut surface singularities from complex numbers to positive characteristic fields, showing that tautness is preserved for most primes and conjecturing a full characterization.

Contribution

It adapts Laufer's transcendental methods to positive characteristic and establishes conditions under which tautness persists across different fields.

Findings

Tautness over  implies tautness over fields of characteristic p for all but finitely many p.

Taut surface singularities with isomorphic dual graphs are mostly taut in positive characteristic.

Conjecture: tautness is characterized precisely by the dual graph in all 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".