Sheaf Of regular functions
Rani Kumari, Umesh Kumar V Dubey
TL;DR
This paper proves that for an affine variety V in affine n-space, the structure sheaf O_V is a sheaf of regular functions, establishing (V, O_V) as a locally ringed space, which is fundamental in algebraic geometry.
Contribution
The paper demonstrates that the structure sheaf on an affine variety is a sheaf of regular functions, confirming the locally ringed space structure.
Findings
O_V is a sheaf of regular functions on V
(V, O_V) forms a locally ringed space
Provides foundational result for affine varieties
Abstract
In this paper, we proved that for an affine variety V in A^n; O_V is a sheaf of regular functions and the ringed space pair (V;O_V ) is a locally ringed space.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications