$\mathbb{K}$-uniruled sets in affine geometry

Abstract

The main goal of this thesis is to study $\mathbb{K}$-uniruled sets that appear in affine geometry. At the beginning we discuss the property of $\mathbb{K}$-uniruledness and its equivalent conditions. Then we bound from above the degree of $\mathbb{K}$-uniruledness of the non-properness set of a polynomial map in terms of its degree and degree of $\mathbb{K}$-uniruledness of the domain variety. At the end we show that some sets associated with the set of fixed points of an algebraic group action are $\mathbb{K}$-uniruled.