# A software package to compute automorphisms of graded algebras

## TL;DR

This paper introduces autgradalg.lib, a Singular library for computing automorphisms of graded algebras, with applications to Mori dream spaces and Fano varieties.

## Contribution

It provides an implementation of algorithms for automorphism computation of graded algebras, extending their application to Mori dream spaces and Fano varieties.

## Key findings

- Successfully computed automorphism groups of several Fano varieties.
- Demonstrated the library's effectiveness on integral, finitely generated graded algebras.
- Extended the applicability of automorphism algorithms to new classes of algebraic varieties.

## Abstract

We present a library autgradalg.lib for the free computer algebra system Singular to compute automorphisms of integral, finitely generated $\mathbb{C}$-algebras that are graded pointedly by a finitely generated abelian group. It implements the algorithms developed in 'Computing automorphisms of Mori dream spaces'. We apply the algorithms to Mori dream spaces and investigate the automorphism groups of a series of Fano varieties.