On Newton-Okounkov bodies, linear series and positivity

On Newton-Okounkov bodies, linear series and positivity

Georg Merz

Doctoral thesis

Date of Examination: 2018-03-08

Date of issue: 2018-04-04

Advisor: Seppänen, Henrik Prof. Dr.

Referee: Seppänen, Henrik Jun.-Prof. Dr.

Referee: Pidstrygach, Viktor Prof. Dr.

Persistent Address: http://hdl.handle.net/11858/00-1735-0000-002E-E3AC-9

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Abstract

English

This thesis consists of four independent articles all connected to the theory of Newton-Okounkov bodies. It contains result about toric degenerations of Del Pezzo surfaces/Bott-Samelson varieties as well as an extension of the theory of Newton-Okounkov bodies of graded linear series.

Keywords: Newton-Okounkov bodies; positivity; toric degeneration