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Toric varieties and their applications
 Klepáč, Adam ; Šťovíček, Jan (advisor) ; Williamson, Jordan (referee)
The thesis provides an introduction into the theory of affine and abstract toric vari- eties. In the first chapter, tools from algebraic geometry indispensable for the compre- hension of the topic are introduced. Many properties of convex polyhedral cones and affine toric varieties are proven and discussed in detail as is the deep connection between the two objects. The second chapter establishes the notion of an abstract variety and translates obtained results to this more general setting, giving birth to the theory of abstract toric varieties and the closely associated theory of fans. Finally, an algorithmic approach to the resolution of singularities on toric surfaces and its relation to continued fractions is revealed. 1
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