2020/07/31 by Paola Frediani, P. Frediani, Juan Carlos Naranjo +3
Mathematics · #Algebraic Geometry and Number Theory #Component (thermodynamics) #Cover (algebra) #Dimension (graph theory) #Fiber #Focus (optics) #Genus #Geodesic #Geometric and Algebraic Topology #Geometry and complex manifolds #Irreducible component #Mathematical analysis #Mathematics #Pure mathematics #Totally geodesic #math.AG #msc:14H40 #msc:14K10
paper · pdf · doi:10.1142/s0219199721500309
Final version. To appear in Communications in Contemporary Mathematics
openalex publication_date 2021/04/02 · arxiv created 2021/05/07 · arxiv updated 2021/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the ramified Prym map [Formula: see text] which assigns to a ramified double cover of a smooth irreducible curve of genus [Formula: see text] ramified in [Formula: see text] points the Prym variety of the covering. We focus on the six cases where the dimension of the source is strictly greater than the dimension of the target giving a geometric description of the generic fiber. We also give an explicit example of a totally geodesic curve which is an irreducible component of a fiber of the Prym map [Formula: see text].