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On the automorphism group of a toral variety

Anton Shafarevich ; Faculty of Computer Science, HSE University, Moscow, Russia
Anton Trushin ; Faculty of Computer Science, HSE University, Moscow, Russia


Puni tekst: engleski pdf 416 Kb

str. 277-291

preuzimanja: 167

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Sažetak

Let \BK be an algebraically closed field of characteristic zero. An affine algebraic variety X over \BK is toral if it is isomorphic to a closed subvariety of a torus (\BK)d. We study the group \Aut(X) of regular automorpshims of a toral variety X. We prove that if T is a maximal torus in \Aut(X), then X is a direct product Y×T, where Y is a toral variety with a trivial maximal torus in the automorphism group. We show that knowing \Aut(Y), one can compute \Aut(X). In the case when the rank of the group \BK[Y]/\BK is dimY+1, the group \Aut(Y) can be described explicitly.

Ključne riječi

Affine variety, invertible function, algebraic torus, automorphism, rigid variety

Hrčak ID:

309003

URI

https://hrcak.srce.hr/309003

Datum izdavanja:

22.10.2023.

Posjeta: 563 *

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