Weierstrass points on Gorenstein curves
type: Item
instance of: scholarly article
title: Weierstrass points on Gorenstein curves
zbMATH Open document ID: 0661.14024
author: Carl Widland
author: Robert F. Lax
published in: Pacific Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The authors investigate which equivalent definitions for Weierstrass points on smooth curves remain equivalent on Gorenstein curves. It is shown that a Wronskian definition using dualizing differentials is equivalent to a definition involving 1-special subschemes with support at a point. The appearance of 1-special subschemes, instead of just special divisors, is to be expected since the limit of a divisor may be a subscheme, but not a divisor, as smooth curves degenerate to a singular curve. Let X denote an integral, projective Gorenstein curve of arithmetic genus \(g>1.\) An example is given to show that there may not be a locally principal 1-special subscheme (i.e. special Cartier divisor) of degree at most g at a (singular) Weierstrass point P on X. Another example is given to show that there may not exist a morphism \(\phi: X\to {\mathbb{P}}^ 1\) of degree at most g such that \(\phi^{-1}(\phi (P))=\{P\}\).
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14M05
zbMATH DE Number: 4079605
zbMATH Keywords: Weierstrass points on smooth curves
zbMATH Keywords: Gorenstein curves
MaRDI profile type: Publication
full work available at URL: pjm.1990.142.197
OpenAlex ID: W2107331300
DOI: 10.2140/PJM.1990.142.197
description: scientific article; zbMATH DE number 4079605