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Transformation groups 2017. Conference dedicated to Prof. Ernest B. Vinberg on the occasion of his 80th birthday
December 17, 2017 09:30–10:20, Moscow, NRU Higher School of Economics, Faculty of Mathematics, room 110
 


Torus actions and trinomials

I. Arzhantsevab

a HSE, Russia
b MSU, Russia

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Abstract: In this talk we discuss algebraic torus actions of complexity one and relate them via Cox rings to affine varieties defined by trinomials. Our aim is to survey recent results on affine trinomial varieties and their automorphism groups.
We study the flexibility property for affine varieties, find all rational trinomial varieties, characterize rigid factorial trinomial hypersurfaces, describe the automorphism group of a rigid trinomial hypersurface, solve some Diophantine equations and characterize existence of certain polynomial curves on trinomial hypersurfaces.
An explicit description of primitive homogeneous locally nilpotent derivations on trimomial affine algebras allows to describe the automorphism group of a complete rational variety with a torus action of complexity one generalizing Demazure's description of the automorphism group of a complete toric variety.

Language: English

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