Birational maps of moduli of Brill-Noether pairs

1997/05/07 by David C. Butler, Butler, David C. · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.alg-geom/9705009

openalex publication_date 1997/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be a smooth projective irreducible curve of genus g. And let G_α(n,d,l) be the moduli space of α stable pairs of a vector bundle of \rank n, °d and a subspace of H⁰(C,E) of dim = l . We find an explicit birational map from G_α (n, d, n+1) to G_α (1, d, n+1) for C general, 1/α≫ 0 and g ≥ n²-1. Because of this and other examples, we conjecture G_α (a, d, a+z) maps birationally to G_α (z, d, a+z) for 1/ α≫ 0 and C general with g>2.

Cited by

• Geometry of linearly stable coherent systems over curves
• Stability of syzygy bundles over certain curves of compact type

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