Explicit analysis of positive dimensional fibres of P_g,r and Xiao conjecture

2021/10/08 by Gian Paolo Grosselli, Grosselli, Gian Paolo, Irene Spelta +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2110.03938

openalex publication_date 2021/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We focus on the positive dimensional fibres of the Prym map P_g,r. We present a direct procedure to investigate infinitely many examples of positive dimensional fibres. Such procedure uses families of Galois coverings of the line admitting a 2-sheeted Galois intermediate quotient. Then we generalize to families of Galois coverings of the line admitting a Galois intermediate quotient of higher degree and we show that the higher degree analogue of the aforementioned procedure gives all the known counterexamples to a conjecture by Xiao on the relative irregularity of a fibration.

Citations

• On the projective normality of complete linear series on an algebraic curve
• Global Prym-Torelli for double coverings ramified in at least 6 points

Related

• The fibers of the Prym map
• Xiao's conjecture for general fibred surfaces
• Global Prym-Torelli for double coverings ramified in at least 6 points
• On the Prym map of Galois covering
• Covering of elliptic curves and the kernel of the Prym map