SEAN KEEL Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA JENIA TEVELEV Department of Mathematics, University of Massachusetts at Amherst, Amherst, MA, 01003, USA
History:
Received 10 May 2008 Revised 11 June 2008
Abstract:
We show that the log canonical bundle, κ, of is very ample, show the homogeneous coordinate ring is Koszul, and give a nice set of rank 4 quadratic generators for the homogeneous ideal: The embedding is equivariant for the symmetric group, and the image lies on many Segre embedded copies of ℙ1 × ⋯ × ℙn-3, permuted by the symmetric group. The homogeneous ideal of is the sum of the homogeneous ideals of these Segre embeddings.
is very ample, show the homogeneous coordinate ring is Koszul, and give a nice set of rank 4 quadratic generators for the homogeneous ideal: The embedding is equivariant for the symmetric group, and the image lies on many Segre embedded copies of ℙ1 × ⋯ × ℙn-3, permuted by the symmetric group. The homogeneous ideal of 
is the sum of the homogeneous ideals of these Segre embeddings.
