2022/08/01 by Francesco Bastianelli, Bastianelli, Francesco, Nicola Picoco +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2208.00990
openalex publication_date 2022/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an irreducible projective variety X, the covering gonality of X is the least gonality of an irreducible curve E⊂ X passing through a general point of X. In this paper we study the covering gonality of the k-fold symmetric product C(k) of a smooth complex projective curve C of genus g≥ k+1. It follows from a previous work of the first author that the covering gonality of the second symmetric product of C equals the gonality of C. Using a similar approach, we prove the same for the 3-fold and the 4-fold symmetric product of C. A crucial point in the proof is the study of Cayley-Bacharach condition on Grassmannians. In particular, we describe the geometry of linear subspaces of ℙn satisfying this condition and we prove a result bounding the dimension of their linear span.