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On rigidity of factorial trinomial hypersurfaces

Ivan Arzhantsev

National Research University Higher School of Economics, Faculty of Computer Science, Kochnovskiy Proezd 3, Moscow, 125319 Russia

E-mail Address: arjantsev@hse.ru

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https://doi.org/10.1142/S0218196716500442Cited by:11 (Source: Crossref)

Abstract

An affine algebraic variety $X$ $X$ is rigid if the algebra of regular functions $𝕂 [X]$ admits no nonzero locally nilpotent derivation. We prove that a factorial trinomial hypersurface is rigid if and only if every exponent in the trinomial is at least $2$ .

The research was supported by the grant RSF-DFG 16-41-01013.

Communicated by H. Schenck

Keywords:

AMSC: Primary: 13A50, Primary: 14R50, Primary: 14R20, Secondary: 14J50, Secondary: 14L30, Secondary: 14M25

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