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Winter 2009 On the projective embeddings of Gorenstein toric del Pezzo surfaces
T. Kikuchi, T. Nakano
Illinois J. Math. 53(4): 1051-1059 (Winter 2009). DOI: 10.1215/ijm/1290435338


We study the projective embeddings of complete Gorenstein toric del Pezzo surfaces by ample complete linear systems, especially of minimal degree and dimension. Complete Gorenstein toric del Pezzo surfaces are in one-to-one correspondence with the 2-dimensional reflexive integral convex polytopes, which are classified into 16 types up to isomorphisms of lattices. Our main result shows that the minimal dimension and the minimal degree of all the ample complete linear systems on such a surface are attained by the primitive anti-canonical class except one case. From this, we determine the projective embeddings of these surfaces which are global complete intersections. We also show that the minimal free resolution of the defining ideal of the image under the anti-canonical embedding of these surfaces is given by an Eagon–Northcott complex.


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T. Kikuchi. T. Nakano. "On the projective embeddings of Gorenstein toric del Pezzo surfaces." Illinois J. Math. 53 (4) 1051 - 1059, Winter 2009.


Published: Winter 2009
First available in Project Euclid: 22 November 2010

zbMATH: 1206.14063
MathSciNet: MR2741177
Digital Object Identifier: 10.1215/ijm/1290435338

Primary: 14J25 , 14M25

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign


Vol.53 • No. 4 • Winter 2009
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