Mapping toric varieties into low dimensional spaces - Dufresne, Emilie; Jeffries, Jack (American Mathematical Society, 2016)
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 variety can be mapped injectively to 2d + 1-dimensional projective space. 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 paper we investigate this question for normal toric varieties, with our most complete results being for Segre-Veronese varieties.