6,074 research outputs found
ACM sets of points in multiprojective space
If X is a finite set of points in a multiprojective space P^n1 x ... x P^nr
with r >= 2, then X may or may not be arithmetically Cohen-Macaulay (ACM). For
sets of points in P^1 x P^1 there are several classifications of the ACM sets
of points. In this paper we investigate the natural generalizations of these
classifications to an arbitrary multiprojective space. We show that each
classification for ACM points in P^1 x P^1 fails to extend to the general case.
We also give some new necessary and sufficient conditions for a set of points
to be ACM.Comment: 21 pages; revised final version; minor corrections; to appear in
Collectanea Mathematic
Star configurations on generic hypersurfaces
Let be a homogeneous polynomial in . Our
goal is to understand a particular polynomial decomposition of ;
geometrically, we wish to determine when the hypersurface defined by in
contains a star configuration. To solve this problem, we use
techniques from commutative algebra and algebraic geometry to reduce our
question to computing the rank of a matrix.Comment: 17 page
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