How much of the Hilbert function do we really need to know?
J\'anos Koll\'ar (Princeton Univ)
TL;DR
This paper explores how, in certain cases, knowing only the leading coefficient of a Hilbert function is sufficient to determine key properties, simplifying the analysis of algebraic structures.
Contribution
It presents examples demonstrating that the leading coefficient of a Hilbert function can sometimes fully determine important algebraic information.
Findings
Leading coefficient suffices in specific cases
Simplifies understanding of Hilbert functions
Provides examples illustrating this phenomenon
Abstract
We describe several examples where the leading coefficient of a Hilbert function tells us everything we need. Based on my lectures at Oberwolfach and Stony Brook.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Analytic Number Theory Research