Invariants of ternary quartics under the action of the orthogonal group
Evelyne Hubert
Inria Côte d’Azur
https://www-sop.inria.fr/members/Evelyne.Hubert/
Date(s) : 16/04/2026 iCal
11h00 - 12h00
Invariants are essential for classifying mathematical objects up to a group of transformations. For a compact Lie group, there is always a finite set of polynomial invariants that separate the orbits. Yet such a set is challenging to compute and can have high cardinality.
Motivated by an application to neuroimaging, we consider here the representation of the group O3(R) on the space of ternary quartics R[x,y,z]_4. We characterize generating and separating sets of rational invariants by their restrictions to a Seshadri slice. These restrictions are invariant under O2(R) or the octahedral group. Their explicit formulae are given by trinomials. The invariants of O3(R) acting on R[x,y,z]_4 can then be obtained in an explicit way, but their numerical evaluation can be achieved more robustly using their restrictions. The exhibited set of invariants futhermore allows us to solve the inverse problem, i.e. find a quartic with prescribed invariants, and the rewriting of any invariants in terms of the generators.
Emplacement
I2M Luminy - TPR2, Amphithéâtre Herbrand 130-134 (1er étage)
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