Prime Fano threefolds of genus 12 with a $G_m$-action

TL;DR

This paper explicitly constructs prime Fano threefolds of genus 12 with a $G_m$-action, classifies their isomorphism types, and analyzes their automorphism groups.

Contribution

It provides a detailed construction and classification of prime Fano threefolds of genus 12 with a $G_m$-action, including their automorphism groups.

Findings

Explicit construction of prime Fano threefolds of genus 12 with $G_m$-action

Classification of isomorphism classes of these threefolds

Description of their automorphism groups

Abstract

We give an explicit construction of prime Fano threefolds of genus 12 with a $G_m$-action, describe their isomorphism classes and automorphism groups.