Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The implicit equation of a multigraded hypersurface   In this article we analyze the implicitization problem of the image of a
rational map $\phi: X --> P^n$, with $T$ a toric variety of dimension $n-1$
defined by its Cox ring $R$. Let $I:=(f_0,...,f_n)$ be $n+1$ homogeneous
elements of $R$. We blow-up the base locus of $\phi$, $V(I)$, and we
approximate the Rees algebra $Rees_R(I)$ of this blow-up by the symmetric
algebra $Sym_R(I)$. We provide under suitable assumptions, resolutions $\Z.$
for $Sym_R(I)$ graded by the torus-invariant divisor group of $X$, $Cl(X)$,
such that the determinant of a graded strand, $\det((\Z.)_\mu)$, gives a
multiple of the implicit equation, for suitable $\mu\in Cl(X)$. Indeed, we
compute a region in $Cl(X)$ which depends on the regularity of $Sym_R(I)$ where
to choose $\mu$. We also give a geometrical interpretation of the possible
other factors appearing in $\det((\Z.)_\mu)$. A very detailed description is
given when $X$ is a multiprojective space.

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The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: econ
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics