Mathematical Sciences: Transcendental Algebraic Geometry

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This research is in the area of transcendental algebraic geometry. It will concern research on "ampleness" and its consequences both in and out of algebraic geometry. In particular, it will concern work on the projective classification of projective varieties. Algebraic geometry is the study of the geometric objects, called algebraic varieties, obtained as solutions of polynomial equations in many variables. Projective space is a completed version of regular space with certain points at infinity added. Classification of algebraic varieties in projective space is one of the old fundamental problems in algebraic geometry.