Discrepancies of non-\Q-Gorenstein varieties

We give an example of a non \Q-Gorenstein variety which is canonical but not klt, and whose canonical divisor has an irrational valuation. We also give an example of an irrational jumping number and we prove that there are no accumulation points for the jumping numbers of normal non-\Q-Gorenstein varieties with isolated singularities.Comment: 12 pages - minor change

A note on the birational geometry of tropical line bundles

Given a closed subvariety Y of a n-dimensional torus, we study how the tropical line bundles of Trop(Y) can be induced by line bundles living on a tropical compactification of Y in a toric variety, following the construction of Jenia Tevelev. We then consider the general structure with respect to the Zariski--Riemann space.Comment: Version

Ample Weil divisors

We define and study positivity (nefness, amplitude, bigness and pseudo-effectiveness) for Weil divisors on normal projective varieties. We prove various characterizations, vanishing and non-vanishing theorems for cohomology, global generation statements, and a result related to log Fano.Comment: Version 3: published versio

Doctor of Philosophy

dissertationWe give an example of a non Q-Gorenstein variety whose canonical divisor has an irrational valuation and an example of a non Q-Gorenstein variety which is canonical but not klt. We also give an example of an irrational jumping number and we prove that there are no accumulation points for the jumping numbers of normal non-Q-Gorenstein varieties with isolated singularities. We prove that the canonical ring of a canonical variety in the sense of [dFH09] is finitely generated. We prove that canonical varieties are klt if and only if R(−KX) is finitely gener-ated. We introduce a notion of nefness for non-Q-Gorenstein varieties and study some of its properties. We then focus on the properties of non-Q-Gorenstein toric varieties, with particular attention to minimal log discrepancies

The Winter\u27s Tale: Problem areas in text and production

This study examines William Shakespeare’s The Winter’s Tale concentrating on what have commonly been perceived to be its problem areas. The play contains a blend of fantasy and realism which has contributed to its divided reception from audiences, critics, and scholars. It is argued that this mixture is not a result of Shakespeare’s failing powers but evidence of a unique and highly theatrical style