Polyhedral divisors of affine trinomial hypersurfaces
Oleg Kruglov
TL;DR
This paper characterizes the torus actions of complexity one on affine trinomial hypersurfaces using polyhedral divisors, providing explicit computations for specific classes like Pham-Brieskorn and rational hypersurfaces.
Contribution
It introduces a method to find polyhedral divisors for these hypersurfaces, advancing the understanding of their torus symmetries and geometric structure.
Findings
Polyhedral divisors are explicitly computed for certain affine trinomial hypersurfaces.
The approach applies to Pham-Brieskorn and rational hypersurfaces.
Provides a framework for analyzing torus actions of complexity one.
Abstract
We find polyhedral divisors corresponding to the torus action of complexity one on affine trinomial hypersurfaces. Explicit computations for particular classes of such hypersurfaces including Pham-Brieskorn surfaces and rational trinomial hypersurfaces are given.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation