Mapping toric varieties into low dimensional spaces

TY - JOUR

T1 - Mapping toric varieties into low dimensional spaces

AU - Dufresne, Emilie

AU - Jeffries, Jack

N1 - This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2016/7/19

Y1 - 2016/7/19

N2 - 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.

AB - 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.

KW - math.AC

KW - math.AG

KW - 13A50, 13D45, 14M25

U2 - 10.1090/tran/7026

DO - 10.1090/tran/7026

M3 - Article

SN - 0002-9947

JO - Transactions of the AMS

JF - Transactions of the AMS

ER -