TL;DR
This paper establishes geometric criteria for certain toric hypersurfaces that ensure the irrationality of specific normal function values at points with maximal unipotent monodromy.
Contribution
It introduces new geometric conditions that guarantee the irrationality of normal function values in the context of toric hypersurfaces.
Findings
Identified geometric conditions leading to irrational normal function values
Proved irrationality at points of maximal unipotent monodromy
Enhanced understanding of the link between geometry and irrationality
Abstract
We exhibit geometric conditions on a family of toric hypersurfaces under which the value of a canonical normal function at a point of maximal unipotent monodromy is irrational.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Commutative Algebra and Its Applications