Towards a geometric approach to Strassen’s asymptotic rank conjecture

• Autores: Austin Conner, Fulvio Gesmundo, J.M. Landsberg, Emanuele Ventura, Yao Wang
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 1, 2021, págs. 63-86
• Idioma: inglés
• DOI: 10.1007/s13348-020-00280-8
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• Resumen

  • We make a first geometric study of three varieties in Cm⊗Cm⊗Cm (for each m), including the Zariski closure of the set of tight tensors, the tensors with continuous regular symmetry. Our motivation is to develop a geometric framework for Strassen’s asymptotic rank conjecture that the asymptotic rank of any tight tensor is minimal. In particular, we determine the dimension of the set of tight tensors. We prove that this dimension equals the dimension of the set of oblique tensors, a less restrictive class introduced by Strassen.