Derivation module and its Poincar\'{e} series of the projective closure of certain affine curves
Joydip Saha, Indranath Sengupta, Pranjal Srivastava
TL;DR
This paper computes the Poincaré series of the derivation module for the projective closure of specific affine monomial curves, advancing understanding of their algebraic structure.
Contribution
It introduces a method to derive the Poincaré series for the derivation module of these curves' projective closures, a novel calculation in algebraic geometry.
Findings
Explicit formulas for the Poincaré series obtained
Enhanced understanding of the derivation modules of affine monomial curves
New techniques applicable to algebraic curve analysis
Abstract
Our aim in this paper is to compute the Poincar\'{e} series of the derivation module of the projective closure of certain affine monomial curves.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Meromorphic and Entire Functions