# Toric weak Fano varieties associated to building sets

## TL;DR

This paper characterizes when the toric varieties linked to building sets are weak Fano, providing a precise criterion based on the structure of the building set.

## Contribution

It offers a complete characterization of weak Fano conditions for toric varieties derived from building sets, filling a gap in the understanding of their geometric properties.

## Key findings

- Provides a necessary and sufficient condition for weak Fano property.
- Connects combinatorial building set structures to geometric Fano conditions.
- Enhances classification of toric varieties associated with building sets.

## Abstract

We give a necessary and sufficient condition for the nonsingular projective toric variety associated to a building set to be weak Fano in terms of the building set.