Smooth Herzog projective curves
Hang Huang, Yevgeniya Tarasova, Matteo Varbaro, Emily Witt
TL;DR
This paper proves that smooth projective curves with a squarefree Groebner degeneration must have genus zero, linking algebraic degenerations to geometric genus.
Contribution
It establishes a new connection between Groebner degenerations and the genus of smooth projective curves, showing a restriction to genus zero.
Findings
Curves with squarefree Groebner degenerations are genus zero.
The result applies to smooth projective curves.
Provides insight into algebraic degenerations and geometric properties.
Abstract
We prove that smooth projective curves admitting a squarefree Groebner degeneration have genus 0.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Commutative Algebra and Its Applications