# Nef partitions for codimension 2 weighted complete intersections

## TL;DR

This paper proves that smooth well-formed Fano weighted complete intersections of codimension 2 admit nef partitions and explores their applications in Mirror Symmetry, including explicit classifications and models for dimensions 4 and 5.

## Contribution

It establishes the existence of nef partitions for a class of Fano weighted complete intersections and provides explicit classifications and models in low dimensions.

## Key findings

- All nef partitions for smooth well-formed Fano weighted complete intersections of dimensions 4 and 5 are listed.
- Weak Landau-Ginzburg models are constructed for these intersections.
- The result has implications for Mirror Symmetry applications.

## Abstract

We prove that a smooth well formed Fano weighted complete intersection of codimension 2 has a nef partition. We discuss applications of this fact to Mirror Symmetry. In particular we list all nef partitions for smooth well formed Fano weighted complete intersections of dimensions 4 and 5 and present weak Landau--Ginzburg models for them.