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Mathematics > Commutative Algebra
Title: Covariant reconstruction of forms from their invariants
(Submitted on 26 Mar 2024 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: Let $K$ be an algebraically closed field of characteristic $0$ and $f$ be a homogeneous polynomial. We provide an explicit algorithm, which, given the invariants of a generic $f$ under the action of $\mathrm{GL}_n(K)$ returns a polynomial in the orbit of $f$. We derive a specific algorithm for the reconstruction of generic non-hyperelliptic curve of genus 4 from their invariants, as well as a direct reconstruction algorithm for generic non-hyperelliptic curves of genus 3 from their Dixmier-Ohno invariants.
Submission history
From: Thomas Bouchet [view email][v1] Tue, 26 Mar 2024 08:42:57 GMT (27kb)
[v2] Wed, 27 Mar 2024 08:28:55 GMT (27kb)
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