Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equations for point configurations to lie on a rational normal curve   The parameter space of $n$ ordered points in projective $d$-space that lie on
a rational normal curve admits a natural compactification by taking the Zariski
closure in $(\mathbb{P}^d)^n$. The resulting variety was used to study the
birational geometry of the moduli space $\overline{\mathrm{M}}_{0,n}$ of
$n$-tuples of points in $\mathbb{P}^1$. In this paper we turn to a more
classical question, first asked independently by both Speyer and Sturmfels:
what are the defining equations? For conics, namely $d=2$, we find
scheme-theoretic equations revealing a determinantal structure and use this to
prove some geometric properties; moreover, determining which subsets of these
equations suffice set-theoretically is equivalent to a well-studied
combinatorial problem. For twisted cubics, $d=3$, we use the Gale transform to
produce equations defining the union of two irreducible components, the
compactified configuration space we want and the locus of degenerate point
configurations, and we explain the challenges involved in eliminating this
extra component. For $d \ge 4$ we conjecture a similar situation and prove
partial results in this direction.

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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org