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On a conjecture of Moreno-Frías and Rosales for numerical semigroups

Masahiro Watari

Abstract

The present paper addresses a semimodule counting conjecture of Moreno-Frías and Rosales for numerical semigroups. Applying Pfister and Steenbrink's Theory for punctual Hilbert schemes of curve singularities, we show that this conjecture is true for any numerical semigroup.

On a conjecture of Moreno-Frías and Rosales for numerical semigroups

Abstract

The present paper addresses a semimodule counting conjecture of Moreno-Frías and Rosales for numerical semigroups. Applying Pfister and Steenbrink's Theory for punctual Hilbert schemes of curve singularities, we show that this conjecture is true for any numerical semigroup.
Paper Structure (3 sections, 7 theorems, 9 equations)

This paper contains 3 sections, 7 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of the main theorem

Key Result

theorem 2

For any numerical semigroup $S$, Conjecture Main conjecture is true with $n_S=F(S)$.

Theorems & Definitions (13)

  • Conjecture 1
  • theorem 2
  • Proposition 3: PS, Theorem 3
  • Corollary 4
  • Remark 5
  • Proposition 6: SW1, Proposition 6
  • Lemma 7
  • proof
  • Remark 8
  • Lemma 9
  • ...and 3 more