Corrigendum to the paper "The Mori fan of the Dolgachev-Nikulin-Voisin family in genus $2$'' by K. Hulek and C. Liese

TL;DR

This corrigendum corrects enumeration errors in HL22 for the maximal cones of the Mori fan of the Dolgachev-Nikulin-Voisin family in genus $2$. It identifies and amends bookkeeping mistakes in the counts of models for types $\mathscr{T}$ and $\mathscr{P}$, using a computer-assisted enumeration complemented by hand verification, and provides updated totals. The corrected counts are $129$ models for type $\mathscr{T}$ and $450$ surfaces for type $\mathscr{P}$, leading to $741$ cones of type $\mathscr{T}$ and $2657$ cones of type $\mathscr{P}$, for a total of $3398$ maximal cones in the Mori fan. The core methodology and theoretical framework of HL22 remain applicable, with the refinements ensuring accurate cone enumeration for downstream mathematical and computational applications.

Abstract

In this note, we correct some of the results of \cite{HL22} concerning the number of maximal cones in the Mori fan of the Dolgachev-Nikulin-Voisin fan in genus $2$. The mistakes in the original paper concern the correct enumeration of cones. The method and the main theoretical results are not affected.

Theorems & Definitions (15)

• Theorem 2.1
• proof
• Theorem 3.1
• proof
• Theorem 3.2
• proof
• Theorem 3.3
• Remark 3.4
• Proposition 4.1
• proof