A combinatorial approach to Alexander-Hirschowitz Theorem based on toric degenerations
Silvia Brannetti
TL;DR
This paper offers a new proof of the Alexander-Hirschowitz Theorem in three dimensions by employing degenerations of toric varieties, providing an alternative geometric approach.
Contribution
It introduces a novel combinatorial method using toric degenerations to prove the Alexander-Hirschowitz Theorem in dimension 3.
Findings
Successful proof of the theorem using toric degenerations
New combinatorial techniques for algebraic geometry
Potential for extending methods to higher dimensions
Abstract
We present an alternative proof of the Alexander-Hirschowitz Theorem in dimension 3 using degenerations of toric varieties.
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Taxonomy
TopicsGraph theory and applications · Advanced Combinatorial Mathematics · Topological and Geometric Data Analysis