On Self-Associated Sets of Points in Small Projective Spaces

Abstract

We study moduli of “self-associated” sets of points in P ⁿ for small n. In particular, we show that for n = 5 a general such set arises as a hyperplane section of the Lagrangian Grassmanian LG(5,10) ⊂ P ¹⁵. For n = 6, a general such set arises as a hyperplane section of the Grassmanian G(2,6) ⊂ 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 P ⁶ and P ⁷, respectively.

Key Words:

• Gorenstein property
• Grassmanians
• Projective geometry

2000 Mathematics Subject Classification:

• 14N05
• 14N20

ACKNOWLEDGMENTS

The author thanks Prof. Lazarsfeld and Prof. Kleiman for helpful suggestions that improved the exposition of the present article.

The author was partially supported by the NSF Graduate Research Fellowship and RTG Grant.

Notes

Communicated by S. Kleiman.

In memory of my grandmother Ludmila.