Betti Tables of Reducible Algebraic Curves
David J. Bruce, Pin-Hung Kao, Evan D. Nash, Ben Perez, and Peter, Vermeire
TL;DR
This paper investigates the Betti tables of reducible algebraic curves, especially line arrangements, providing formulas for various genus cases and a general method for certain line arrangements.
Contribution
It introduces a general formula for the quadratic strand of Betti tables of specific line arrangements and explicit formulas for genus zero and one curves.
Findings
Derived formulas for Betti tables of genus zero and one curves
Provided a general formula for quadratic strands in certain line arrangements
Extended formulas to some higher genus curves
Abstract
We study the Betti tables of reducible algebraic curves with a focus on connected line arrangements and provide a general formula for computing the quadratic strand of the Betti table for line arrangements that satisfy certain hypotheses. We also give explicit formulas for the entries of the Betti tables for all curves of genus zero and one. Last, we give formulas for the graded Betti numbers for a class of curves of higher genus.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Algebraic Geometry and Number Theory