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Stable sheaves on a smooth quadric surface with linear Hilbert bipolynomials.

Edoardo Ballico¹, Sukmoon Huh²

¹Università di Trento, 38123 Povo, Italy.

Thescientificworldjournal

|March 28, 2014

Summary

This study explores stable sheaves on quadric surfaces, detailing their geometric properties using Hilbert bipolynomials and locally free resolutions for specific cases.

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Area of Science:

Algebraic Geometry
Mathematical Physics

Background:

Moduli spaces are crucial for classifying mathematical objects.
Stable sheaves on surfaces provide a rich area of study in algebraic geometry.

Purpose of the Study:

To investigate the geometry of moduli spaces of stable sheaves on a smooth quadric surface.
To analyze these spaces in special cases involving linear Hilbert bipolynomials.

Main Methods:

Utilizing the theory of stable sheaves.
Applying Hilbert bipolynomials to describe sheaf properties.
Analyzing geometric structures via locally free resolutions.

Main Results:

Characterization of moduli spaces for specific stable sheaves.
Description of the geometry in terms of sheaf resolutions.
Identification of special cases with linear Hilbert bipolynomials.

Conclusions:

The geometry of these moduli spaces is intrinsically linked to the algebraic properties of the sheaves.
Locally free resolutions offer a powerful tool for understanding moduli spaces on quadric surfaces.