Compactifications of Hurwitz spaces

2012/06/20 by Anand Deopurkar, Deopurkar, Anand
Mathematics · #14H10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1206.4535

openalex publication_date 2012/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct several modular compactifications of the Hurwitz space H^d_g/h of genus g curves expressed as d-sheeted, simply branched covers of genus h curves. These compactifications are obtained by allowing the branch points of the covers to collide to a variable extent. They are very well-behaved if d = 2, 3, or if relatively few collisions are allowed. We recover as special cases the spaces of twisted admissible covers of Abramovich, Corti and Vistoli and the spaces of hyperelliptic curves of Fedorchuk.

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