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Computing GIT-fans with symmetry and the Mori chamber decomposition of \(\overline{M}_{0,6}\). (English) Zbl 1442.14146

Summary: We propose an algorithm to compute the GIT-fan for torus actions on affine varieties with symmetries. The algorithm combines computational techniques from commutative algebra, convex geometry, and group theory. We have implemented our algorithm in the SINGULAR library GITFAN.LIB. Using our implementation, we compute the Mori chamber decomposition of \(\mathrm{Mov}(\overline{M}_{0,6})\).

MSC:

14L24 Geometric invariant theory
13A50 Actions of groups on commutative rings; invariant theory
14Q99 Computational aspects in algebraic geometry
14H10 Families, moduli of curves (algebraic)
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
14-04 Software, source code, etc. for problems pertaining to algebraic geometry
14E30 Minimal model program (Mori theory, extremal rays)
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References:

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