2020/06/10 by János Nagy, Nagy, János
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2006.05869
openalex publication_date 2020/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the classical case of irreducible smooth algebraic curves every genus 2 curve is hyperelliptic, or in other words there is a complete linear series g21 on them. On the other hand if g > 2, then a generic smooth curve of genus 2 is nonhyperelliptic. In this article we investigate the situation of normal surface singularities, so we fix a resolution graph T and a generic singularity with resolution \tX corresponding to it in the sense of \citeNNII. We consider an integer effective cycle Z on the resolution \tX and investigate the existence of a complete linear series g21 on it. The article has the main motivation that we will use heavily the results in it to compute the class of the image varieties of Abel maps in a following manuscript.