The singular set of triholomorphic maps into quartic K3 surface

TL;DR

This paper proves that weakly triholomorphic maps from compact hyperk"ahler surfaces to certain algebraic K3 surfaces have only isolated singularities, advancing understanding of their regularity properties.

Contribution

It establishes the isolated singularity property for weakly triholomorphic maps into quartic K3 surfaces, a new result in the study of hyperk"ahler geometry.

Findings

Weakly triholomorphic maps have only isolated singularities.

The target K3 surface is defined by a degree 4 polynomial in projective space.

The result applies to maps from compact hyperk"ahler surfaces.

Abstract

We prove that any weakly triholomorphic map from a compact hyperk\"ahler surface to an algebraic K3 surface defined by a homogeneous polynomial of degree 4 in $\mathbb{C}P^3$ has only isolated singularities.