ENRICHED ENUMERATIVE GEOMETRY

Abstract

Enumerative geometry is the subfield of algebraic geometry concerned with counting the number of solutions to geometric questions. Classically one restricts to working over algebraically closed fields to get invariant answers to such problems. Enriched enumerative geometry uses tools from motivic homotopy theory (i.e., homotopy theory for schemes) to obtain invariant results over more general fields. In this paper, we give an overview of some standard techniques from enumerative geometry, both classical and enriched. We then restrict our attention to the problem of counting the number of lines of the complete intersection of two degree n − 2 hypersurfaces in Pnk when n is even.