Points in projective spaces and applications

Points in Projective Spaces and Applications

Abstract. We prove that points of a finite subset Σ ⊂ P impose independent linear conditions on homogeneous forms on P of degree ⌊nλ/2 − n⌋ in the case when at most λk points of the set Σ lie on a possibly reducible curve in P of degree k and |Σ| < λ⌈λ/2⌉, where λ is a natural number and n > 3. We apply the obtained result to threefolds having at most isolated ordinary double points. In particu...

Koszul Configurations of Points in Projective Spaces

We prove a new criterion for the homogeneous coordinate ring of a finite set of points in Pn to be Koszul. Like the well known criterion due to Kempf [7] it involves only incidence conditions on linear spans of subsets of a given set. We also give a sufficient condition for the Koszul property to be preserved when passing to a subset of a finite set of points in Pn.

Hilbert Schemes of Points in Projective Spaces

Biquaternions Lie Algebra and Complex-Projective Spaces

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On Self-associated Sets of Points in Small Projective Spaces

We study moduli of “self-associated” sets of points in P 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) ⊂ P (this was conjectured by Eisenbud-Popescu in 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) ⊂ P. We also ...