Poncelet curves and associated theta characteristics
type: Item
instance of: scholarly article
title: Poncelet curves and associated theta characteristics
zbMATH Open document ID: 0646.14025
published in: Expositiones Mathematicae
publication date: 1988-01-01T00:00:00Z
review text: Poncelet's theorem states that if a regular conic S contains \(c+1\) points such that the \(\binom{c+1}{2}\) points of intersection of their tangents lie on an algebraic curve C of degree c, then there is an infinity of such divisors on S with the same property. The author reexamines the result in the light of recent joint work with \textit{M. S. Narasimhan} on the moduli scheme of stable rank 2 bundles on projective 3-space (related to the theory of instanton bundles). In the author's words: ``Besides an alternative elementary proof of Darboux' theorem (the work) reveals several new features of the Poncelet relations together with some practical advantages: (1) The equations of the Poncelet curves can be characterized by Plücker relations of their coefficients... (2) The equations are at the same time determinants of special persymmetric (or Hankel) matrices of linear forms, which define unique associated Theta characteristics on the Poncelet curves. (3) The matrix description yields a direct and explicit bijection between the equations and the linear systems on the conic...''
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 14K25
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 4053793
zbMATH Keywords: Poncelet's theorem
zbMATH Keywords: instanton bundles
zbMATH Keywords: Poncelet curves
zbMATH Keywords: Plücker relations
zbMATH Keywords: Theta characteristics
author: Günther Trautmann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4053793