Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P 1 , a plane cubic, or a space quartic. For each form, a certain syzygy from classical invariant theory gives the curve's jacobian in Weierstrass form and the covering map to its jacobian induced by the K
Coherent systems on a nodal curve of genus one
β Scribed by Usha N. Bhosle
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 210 KB
- Volume
- 284
- Category
- Article
- ISSN
- 0025-584X
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β¦ Synopsis
Abstract
We study coherent systems on an irreducible nodal curve of arithmetic genus 1. We determine conditions for their nonβemptiness and study properties like irreducibility, smoothness, seminormality and rationality.
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