Karim Adiprasito: Genericity in algebraic geometry

Abstract

A common feature of theorems in geometry is that they apply under for a sufficiently "generic" object on a fixed space (think theorems of Morse-Sard or Lefschetz, for instance). Conversely, one could ask under which conditions it makes sense to speak of a "generic" space, and what properties it enjoys. Toric varieties are among the classes of varieties for which the notion of a "generic" realization makes sense. I will explain what I mean by that, some of the properties generic toric varieties enjoy, and some applications to old problems.