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A software package to compute automorphisms of graded algebras. (English) Zbl 1404.13005

Summary: We present {autgradalg.lib}, a Singular library to compute automorphisms of integral, finitely generated \(\mathbb{C}\)-algebras that are graded pointedly by a finitely generated abelian group. The library implements algorithms of J. Hausen et al. [Math. Comput. 86, No. 308, 2955–2974 (2017; Zbl 1401.14200)]. We apply these to Mori dream spaces and investigate the automorphism groups of a series of Fano varieties.

MSC:

13A02 Graded rings
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
14J50 Automorphisms of surfaces and higher-dimensional varieties
14L30 Group actions on varieties or schemes (quotients)
14Q15 Computational aspects of higher-dimensional varieties
13A50 Actions of groups on commutative rings; invariant theory

Citations:

Zbl 1401.14200
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References:

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[8] 10.1016/j.jsc.2013.01.005 · Zbl 1277.13001 · doi:10.1016/j.jsc.2013.01.005
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