The defect of Fano 3-folds

TL;DR

This paper investigates the defect of terminal Gorenstein Fano 3-folds, establishing bounds based on Picard rank and the presence of planes, contributing to the classification of these algebraic varieties.

Contribution

It provides new bounds on the defect of terminal Gorenstein Fano 3-folds with Picard rank 1, especially those without planes, and offers methods to study cases with planes.

Findings

Bound on defect for Picard rank 1 Fano 3-folds without planes

General bound for quartic 3-folds

Methodology for studying defect in presence of planes

Abstract

This paper studies the defect of terminal Gorenstein Fano 3 folds. I determine a bound on the defect of terminal Gorenstein Fano 3-folds of Picard rank 1 that do not contain a plane. I give a general bound for quartic 3-folds and indicate how to study the defect of terminal Gorenstein Fano 3-folds with Picard rank 1 that contain a plane.