Kanev and Todorov surfaces in toric 3-folds

Abstract

In the first part of this article we show for some examples of surfaces of general type in toric 3-folds how to construct minimal and canonical models by toric methods explicitly. The examples we study will turn out to be so called Kanev surfaces and surfaces similar to Todorov surfaces. In the second part of this article we study further properties of these examples of surfaces by toric methods: We compute the singularities of the canonical models and compute the generic Picard numbers.