# Strong full exceptional collections on certain toric varieties with Picard number three via mutations

## TL;DR

This paper constructs strong full exceptional collections for specific toric varieties with Picard number three, using blow-up techniques and mutations, advancing understanding of their derived categories.

## Contribution

It introduces a method to build strong full exceptional collections on certain toric varieties with Picard number three via mutations and Orlov's blow-up formula.

## Key findings

- Constructed strong full exceptional collections for targeted toric varieties.
- Applied mutations and Orlov's formula to derive these collections.
- Enhanced understanding of derived categories for these toric varieties.

## Abstract

In this paper, we study derived categories of certain toric varieties with Picard number three that are blowing-up another toric varieties along their torus invariant loci of codimension at most three. We construct strong full exceptional collections by using Orlov's blow-up formula and mutations.