Newton Binomial Formulas in Schubert Calculus
Jorge Cordovez, Letterio Gatto, Taise Santiago
TL;DR
This paper extends Newton's binomial formulas to Schubert Calculus, enabling the calculation of specific enumerative geometric problems related to linear series on the projective line with prescribed ramification.
Contribution
It introduces Newton binomial formulas within Schubert Calculus to solve enumerative problems involving linear series with prescribed ramification.
Findings
Derived explicit formulas for enumerating linear series with ramification
Connected classical binomial identities to geometric enumeration
Provided tools for calculating base point free linear series counts
Abstract
We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry