A note on the Picard number of singular Fano 3-folds

TL;DR

This paper establishes an upper bound of 6 on the Picard number for non-smooth Fano 3-folds with isolated factorial canonical singularities, using a construction by Casagrande.

Contribution

It provides a new bound on the Picard number for a specific class of singular Fano 3-folds, extending previous understanding.

Findings

Picard number of such Fano 3-folds is at most 6

Uses Casagrande's construction to derive the bound

Advances classification of singular Fano 3-folds

Abstract

Using a construction due to C. Casagrande and further developed by the author, we prove that the Picard number of a non-smooth Fano 3-fold with isolated factorial canonical singularities, is at most 6.