# Real nodal sextics without real nodes

## TL;DR

This paper classifies irreducible sextic curves in real projective plane with only non-real nodes, using K3 surface periods and Nikulin's lattice involution classification, extending previous classifications of smooth sextics.

## Contribution

It provides a rigid isotopy classification for sextic curves with non-real nodes, generalizing Nikulin's work on smooth sextics in the real projective plane.

## Key findings

- Classification of such sextic curves achieved
- Use of K3 surface periods and lattice involutions
- Extension of previous smooth sextic classifications

## Abstract

We present a rigid isotopy classification of irreducible sextic curves in $\mathbb{RP}^2$ which have non-real ordinary double points as their only singularities. Our approach uses periods of K3 surfaces and V. Nikulin's classification of involutions with condition on unimodular lattices. The classification obtained generalizes Nikulin's rigid isotopy classification of non-singular sextics in $\mathbb{RP}^2$.