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Mathematics > Algebraic Geometry

arXiv:1807.09550 (math)
[Submitted on 25 Jul 2018 (v1), last revised 19 Sep 2019 (this version, v3)]

Title:Special apolar subset: the case of star configurations

Authors:Iman Bahmani Jafarloo, Enrico Carlini
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Abstract:In this paper we consider a generic degree $d$ form $ F $ in $n+1$ variables. In particular, we investigate the existence of star configurations apolar to $F$, that is the existence of apolar sets of points obtained by the $ n $-wise intersection of $ r $ general hyperplanes of $ \mathbb{P}^n $. We present a complete answer for all values of $(d,r,n)$ except for $(d,d+1,2)$ when we present an algorithmic approach.
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14T05, 13P05, 14N20
Cite as: arXiv:1807.09550 [math.AG]
  (or arXiv:1807.09550v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.09550

Submission history

From: Iman Bahmani Jafarloo [view email]
[v1] Wed, 25 Jul 2018 12:34:41 UTC (15 KB)
[v2] Wed, 24 Apr 2019 16:57:19 UTC (10 KB)
[v3] Thu, 19 Sep 2019 08:14:31 UTC (11 KB)
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