Projective and birational geometry of Grassmannians and other special varieties

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.

arXiv comment141 pages, Ph.D. Thesis submitted to IMPA. Based on the work of this thesis I was able to submit three preprints: Non-Secant Defectivity via Osculating Projections; On non-secant defectivity of Segre-Veronese varieties; Spherical blow-ups of Grassmannians and Mori Dream Spaces. The present thesis has more examples and some proofs are more detailed than on the papers

References in corpus (9)

• Computing symmetric rank for symmetric tensors
• On blowing up the weighted projective plane
• Varieties with quadratic entry locus, II
• On the number of Waring decompositions for a generic polynomial vector
• Cox rings of cubic surfaces and Fano threefolds
• Scorza quartics of trigonal spin curves and their varieties of power sums
• Computing GIT-fans with symmetry and the Mori chamber decomposition of ${\bar{M}}_{0,6}$
• On the classification of defective threefolds
• On the osculatory behaviour of higher dimensional projective varieties

Cited by in corpus (2)

• The Hitchhiker guide to: Secant Varieties and Tensor Decomposition
• Spherical blow-ups of Grassmannians and Mori Dream Spaces