منابع مشابه
Theta Characteristics and Their Moduli
Theta characteristics appeared for the first time in the context of characteristic theory of odd and even theta functions in the papers of Göpel [Go] and Rosenhain [Ro] on Jacobi’s inversion formula for genus 2. They were initially considered in connection with Riemann’s bilinear addition relation between the degree two monomials in theta functions with characteristics. Later, in order to syste...
متن کاملCharacterizing Curves by Their Odd Theta-characteristics
Consider, for every g ≥ 4, a non-singular, complex, canonical curve of genus g, that is, a curve X embedded in P by its complete canonical series |ωX |. Each such a curve possesses 2 2g line bundles L of degree g − 1 such that L = ωX , the theta-characteristics of X, and precisely Ng := ( 2 2 ) of them are odd (i.e. h(X,L) is odd). To a non-zero section σ of a theta-characteristic one associate...
متن کاملUnitons and Their Moduli
We sketch the proof that unitons (harmonic spheres in U(N)) correspond to holomorphic ‘uniton bundles’, and that these admit monad representations analogous to Donaldson’s representation of instanton bundles. We also give a closed-form expression for the unitons involving only matrix operations, a finite-gap result (two-unitons have energy ≥ 4), computations of fundamental groups of energy ≤ 4 ...
متن کاملModuli of metaplectic bundles on curves and Theta-sheaves
Historically θ-series have been one of the major methods of constructing automorphic forms. A representation-theoretic appoach to the theory of θ-series, as discoved by A. Weil [18] and extended by R. Howe [12], is based on the oscillator representation of the metaplectic group (cf. [17] for a recent survey). In this paper we propose a geometric interpretation this representation (in the nonram...
متن کاملModuli Spaces of Abelian Surfaces : Compactification , Degenerations , and Theta Functions (
theory of Lie groups—but many geometric questions lead to non-standard problems which go beyond, or lie on the frontiers of, standard theory. Such questions arise both in reassuringly down-to-earth topics like the existence of constant mean curvature surfaces in R, and in more esoteric ones such as the use of harmonic maps into 'buildings', which have been exploited by Gromov and Schoen to obta...
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ژورنال
عنوان ژورنال: Milan Journal of Mathematics
سال: 2012
ISSN: 1424-9286,1424-9294
DOI: 10.1007/s00032-012-0178-7