Vector bundles and the icosahedron

نویسنده

  • Nigel Hitchin
چکیده

Describing the equation of a plane curve C as the determinant of a matrix of linear forms is a classical problem. A related issue is expressing C as the Pfaffian of a skewsymmetric matrix of forms. When the curve is defined by a harmonic homogeneous polynomial (a solution to Laplace’s equation), then the action of the Lie algebra of the orthogonal group SO(3,C) provides a natural such expression, and with it, a natural semi-stable rank two vector bundle E on C. This paper concerns itself with these bundles, which have trivial determinant and H(C,E) = 0.

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تاریخ انتشار 2009