Projective and birational geometry of Grassmannians and other special varieties

TL;DR

This thesis explores the secant defectivity of projective varieties and investigates the birational geometry of blow-ups of Grassmannians at points, combining classical invariants with modern algebraic geometry techniques.

Contribution

It introduces new insights into secant defectivity and the birational properties of Grassmannian blow-ups, bridging classical and modern algebraic geometry.

Findings

Characterization of secant defectivity in certain varieties

Analysis of birational transformations of Grassmannian blow-ups

Identification of geometric properties influencing defectivity

Abstract

In the first part of the thesis, we study a classical invariant of projective varieties, the secant defectivity. The second part is devoted to modern algebraic geometry, we study the birational geometry of blow-ups of Grassmannians at points.