On the higher Wahl maps
type: Item
instance of: scholarly article
title: On the higher Wahl maps
zbMATH Open document ID: 0833.14022
author: Akira Ohbuchi
published in: Tsukuba Journal of Mathematics
publication date: 1994-12-19T00:00:00Z
review text: Let \(C\) be a complete nonsingular curve of genus \(g\) over an algebraically closed field \(k\), and \({\mathcal L}\) an invertible sheaf over \(C\) of positive degree. Generalising a construction of \textit{J. Wahl} [J. Differ. Geom. 32, No. 1, 77-98 (1990; Zbl 0724.14022)] the author defines a map \[ \Phi^{(n)} : \bigwedge^n \Gamma (C, {\mathcal L}) \to \Gamma (C, \omega_C^{ \otimes 1/2n (n - 1)} \otimes {\mathcal L}^{\otimes n}) \] whose surjectivity is related to linear normality of generalised dual curves of \(C\). His main theorem states that if \(\text{char} k > \deg {\mathcal L} > (g - 1) (2n^2 - 2n + 3) + 2(n^2 - 1)\) then \(\Phi^{(n)}\) is surjective. The proof seems to be similar to arguments in Wahl's paper; the presentation of the paper is rather formal.
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14E25
zbMATH DE Number: 701549
zbMATH Keywords: Wahl map
zbMATH Keywords: dual curves
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496162456
OpenAlex ID: W2620257939
DOI: 10.21099/TKBJM/1496162456
description: scientific article; zbMATH DE number 701549