The projective analytic spectrum of the double of a module

TL;DR

This paper studies the properties of the projective analytic spectrum of the double of a module and applies these findings to a specific algebraic geometric setting involving hypersurfaces and curves.

Contribution

It introduces new properties of the projectivized analytic spectrum of module doubles and applies them to a particular algebraic geometric context.

Findings

Established general properties of the projective analytic spectrum of module doubles.

Applied these properties to the case of $ ext{Projan}( ext{R}(( ext{JM}(X))_D))$ over an irreducible curve.

Provided insights into the structure of spectra in algebraic geometry.

Abstract

In this work, we investigate the projectivized analytic spectrum of the double of a module, establishing some general properties, and we apply these results to $\mbox{Projan}(\cR((JM(X))_D))$ over the origin in $C\times C$, where $C$ is an irreducible curve in a hypersurface $X$.