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Ehemalige Mitarbeiter

Dr. Christian Ikenmeyer

Lupe

Kontakt
University of Liverpool
Department of Computer Science
Ashton Building, Office 311
Ashton Street, Liverpool, L69 3BX
United Kingdom
 
Persönliche Homepage
http://pcwww.liv.ac.uk/~iken/

Publikationen in der Arbeitsgruppe

Fundamental invariants of orbit closures
Citation key BI-Fundamental-Invariants-Of-Orbit-Closures
Author Peter Bürgisser and Christian Ikenmeyer
Pages 390–434
Year 2017
DOI 10.1016/j.jalgebra.2016.12.035
Journal Journal of Algebra
Volume 477
Month 05
Note Available online, to appear soon
Abstract For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental SL-invariant function that relates the coordinate ring of the orbit with the coordinate ring of its closure. For the power sums we can write down this fundamental invariant explicitly in most cases. Our constructions generalize the two Aronhold invariants on ternary cubics. For the other objects we identify the invariant function conditional on intriguing combinatorial problems much like the well-known Alon-Tarsi conjecture on Latin squares. We provide computer calculations in small dimensions for these cases. As a main tool for our analysis, we determine the stabilizers, and we establish the polystability of all the mentioned forms and tensors (including the generic ones).
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