The Spectral Construction for a (1,8)-Polarized Family of Abelian Varieties

2009/03/31 by Anthony Bak, Bak, A. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.0903.5488

openalex publication_date 2009/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the Spectral Construction, a technique used with great success to study and construct vector bundles on elliptically fibered varieties, to a special family of abelian surface fibered varieties. The results are motivated by requirements from Heterotic String Phenomenology where vector bundles with specified chern class are required to produce a realistic particle spectrum. Although only certain (1,8)-polarized families of abelian surfaces are considered here we expect the main ideas to carry over to other families of abelian varieties with a uniform relative polarization type.

Citations

• Langlands duality for Hitchin systems

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