Publication Date

2019-04-26

Availability

Open access

Embargo Period

2019-04-26

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PHD)

Department

Mathematics (Arts and Sciences)

Date of Defense

2019-04-03

First Committee Member

Shulim Kaliman

Second Committee Member

Bruno De Oliveira

Third Committee Member

Morgan Brown

Fourth Committee Member

Rafael Nepomechie

Abstract

We consider n - dimensional, with n greater or equal to 4, flexible quasi-affine varieties X, that are varieties on which the group generated by all one-parameter unipotent subgroups of Aut(X) acts transitively. We prove that for any subvariety Y of X, isomorphic to a line, every SL(n) - automorphism of the normal bundle of Y is induced by a global automorphism of X. We also extend this result also to automorphisms of jet bundles on Y.

Keywords

Extension problem; flexible varieties

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