A chain rule formula for higher derivations and inverses of polynomial maps

• Verfasst von: Maurischat, Andreas [VerfasserIn]
• Titel: A chain rule formula for higher derivations and inverses of polynomial maps
• Verf.angabe: Andreas Maurischat
• Fussnoten: Gesehen am 25.02.2019
• Titel Quelle: Enthalten in: De.arxiv.org
• Jahr Quelle: 2016
• Band/Heft Quelle: (2016) Artikel-Nummer 1611.01940, 15 Seiten
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1588022846

Abstract

The multidimensional chain rule formula for analytic functions and its generalisation to higher derivatives perfectly work in the algebraic setting in characteristic zero. In positive characteristic one runs into problems due to denominators in these formulas. In this article we show a direct analog of these formulas using higher derivations which are defined in any characteristic. We also use these formulas to show how higher derivations to different coordinate systems are related to each other. Finally, we apply this to polynomial automorphisms in arbitrary characteristic and obtain a formula for the inverse of such a polynomial automorphism.