Sarkisov links for index 1 Fano 3-folds in codimension 4

TL;DR

This paper classifies Sarkisov links originating from index 1 Fano 3-folds embedded in codimension 4, and uses this classification to determine the Picard rank of numerous such Fano 3-folds.

Contribution

It provides a classification of Sarkisov links for a specific class of Fano 3-folds and computes their Picard ranks, advancing understanding of their birational geometry.

Findings

Classification of Sarkisov links from Type I Tom centres

Determination of Picard ranks for many Fano 3-folds

Enhanced understanding of the birational structure of these Fano varieties

Abstract

We classify Sarkisov links from index 1 Fano 3-folds anticanonically embedded in codimension 4 that start from so-called Type I Tom centres. We apply this to compute the Picard rank of many such Fano 3-folds.