Mapping toric varieties into small dimensional spaces

Emilie Dufresne, University of Nottingham. Part of the algebra seminars series.

A smooth d-dimensional projective variety X can always be embedded into 2d + 1-dimensional space. In contrast, a singular variety may require an arbitrary large ambient space. If we relax our requirement and ask only that the map is injective, then any d-dimensional projective (resp. affine) variety can be mapped injectively to 2d + 1-dimensional projective space (resp. affine).

A natural question then arises: what is the minimal m such that a projective variety can be mapped injectively to m-dimensional projective space? In this talk I discuss this question for the afffine cones over normal toric varieties, with the most complete results being for the affine cones over Segre-Veronese varieties.

Emilie Dufresne, University of Nottingham