Poncelet curves and associated theta characteristics
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...''
scientific article; zbMATH DE number 4053793
scientific article