Hilbert basis of the Lipman semigroup

TL;DR

This paper introduces a new combinatorial method for computing the Hilbert basis of the Lipman semigroup associated with normal surface singularities, simplifying previous invariant-based calculations.

Contribution

It provides a purely combinatorial approach to determine the Hilbert basis, avoiding complex invariant computations of the ring.

Findings

Simplifies the computation of the Hilbert basis

Eliminates the need for invariant calculations

Offers a more efficient combinatorial method

Abstract

In this work, we give a new method to compute the Hilbert basis of the semigroup of certain positive divisors supported on the exceptional divisor of a normal surface singularity. Our approach is purely combinatorial which permits to avoid the long calculation of the invariants of the ring as it is presented in the work of Altinok and Tosun.