Add to ORKGdissertationThe focus of this dissertation is on birational geometry in characteristic zero. In particular, we consider the notion of generalized pairs, first introduced by Birkar and Zhang. As generalized pairs appear as the base of log Calabi-Yau fibrations, it is important to develop their theory and study their properties. This dissertation consists of two main parts, and each one of them investigates the properties of generalized pairs in a different direction. In the first part, which is the content of Chapter 5, we study some boundedness properties of generalized pairs. More precisely, we try to extend recent results of Hacon, McKernan and Xu about varieties of log general type to generalized pairs. In particular, we show that this e...
In [15], we established a series of correspondences relating five enumerative theories of log Calabi...
This work develops a method to canonically compactify mirror families for positive pairs (Y,D), wher...
Let $(X, \Delta)$ be a projective log canonical Calabi-Yau pair and $L$ an ample $\mathbb{Q}$-line b...
I will discuss joint work with Gabriele Di Cerbo on boundedness of Calabi-Yau pairs. Given an ellip...
We establish a Koll\'ar-type gluing theory for generalized log canonical pairs associated with crepa...
We give an explicit example of log Calabi-Yau pairs that are log canonical and have a linearly decre...
This thesis aims to generalise the theory of complements to log canonical Fano varieties and relate ...
Thesis (Ph.D.)--University of Washington, 2016-06Singularities of algebraic varieties have been stud...
In this thesis we address several questions related to important conjectures in birational geometry....
In 2008, Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-folds $X$ usin...
In the first part of this thesis we give a complete classification of relative log canonical models ...
Abstract. We classify log-canonical pairs (X,∆) of dimension two with KX+∆ an ample Cartier divisor ...
We show that given any two minimal models of a generalized lc pair, there exist small birational mod...
A classical result in birational geometry, Mori’s Cone Theorem, implies that if the canonical bundle...
Algebraic geometry has for many decades been one of the core disciplines of mathematics, and the sub...
In [15], we established a series of correspondences relating five enumerative theories of log Calabi...
This work develops a method to canonically compactify mirror families for positive pairs (Y,D), wher...
Let $(X, \Delta)$ be a projective log canonical Calabi-Yau pair and $L$ an ample $\mathbb{Q}$-line b...
I will discuss joint work with Gabriele Di Cerbo on boundedness of Calabi-Yau pairs. Given an ellip...
We establish a Koll\'ar-type gluing theory for generalized log canonical pairs associated with crepa...
We give an explicit example of log Calabi-Yau pairs that are log canonical and have a linearly decre...
This thesis aims to generalise the theory of complements to log canonical Fano varieties and relate ...
Thesis (Ph.D.)--University of Washington, 2016-06Singularities of algebraic varieties have been stud...
In this thesis we address several questions related to important conjectures in birational geometry....
In 2008, Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-folds $X$ usin...
In the first part of this thesis we give a complete classification of relative log canonical models ...
Abstract. We classify log-canonical pairs (X,∆) of dimension two with KX+∆ an ample Cartier divisor ...
We show that given any two minimal models of a generalized lc pair, there exist small birational mod...
A classical result in birational geometry, Mori’s Cone Theorem, implies that if the canonical bundle...
Algebraic geometry has for many decades been one of the core disciplines of mathematics, and the sub...
In [15], we established a series of correspondences relating five enumerative theories of log Calabi...
This work develops a method to canonically compactify mirror families for positive pairs (Y,D), wher...
Let $(X, \Delta)$ be a projective log canonical Calabi-Yau pair and $L$ an ample $\mathbb{Q}$-line b...