Publication Date

2017-07-21

Availability

Open access

Embargo Period

2017-07-21

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PHD)

Department

Mathematics (Arts and Sciences)

Date of Defense

2017-05-30

First Committee Member

Bruno De Oliveira

Second Committee Member

Shulim Kaliman

Third Committee Member

Morgan Brown

Fourth Committee Member

Fedor Bogomolov

Abstract

We study the relationships between the algebra of symmetric twisted differentials, the algebra generated by tangentially homogeneous polynomials and the quadric algebra of a smooth projective subvariety whose codimension is small relative to its dimension. It is conjectured that these three algebras coincide for such varieties and we prove this for complete intersections and subvarieties of codimension two. The connection between these three algebras leads to questions about the local projective differential geometry of the variety, its trisecant lines and the linear system of quadrics vanishing on it.

Keywords

Symmetric twisted differentials; quadrics; symmetric tensors; projective subvariety; hartshorne conjecture

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