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From arXiv

On self-associated sets of points in small projective spaces

We study moduli of ``self-associated'' sets of points in

{\bf P}^n

for small

n

. In particular, we show that for

n=5

a general such set arises as a hyperplane section of the Lagrangean Grassmanian

LG(5,10) \subset {\bf P}^{15}

(this was conjectured by Eisenbud-Popescu in {\it Geometry of the Gale transform}, J. Algebra 230); for

n=6

, a general such set arises as a hyperplane section of the Grassmanian

G(2,6) \subset {\bf P}^{14}

. We also make a conjecture for the next case

n=7

. Our results are analogues of Mukai's characterization of general canonically embedded curves in

{\bf P}^6

and

{\bf P}^7

, resp.

Simplify

Published on April 24, 2006

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