Nettet23. aug. 2024 · By Otto's Lectures on Riemann surfaces, p.139, the divisor of a non-vanishing meromorphic 1-form on a compact Riemann surface of genus g satisfies … NettetLine Bundles on Super Riemann Surfaces . Abstract . We give the elements of a theory of line bundles, their classification, and their connec-tions on super Riemann …
Holomorphic line bundles on a punctured disc - MathOverflow
Nettet24. mar. 2024 · A line bundle is a special case of a vector bundle in which the fiber is either , in the case of a real line bundle, or , in the case of a complex line bundle. … NettetWe give the elements of a theory of line bundles, their classification, and their connections on super Riemann surfaces. There are several salient departures from … lititz winter festival
algebraic geometry - Holomorphic line bundle with degree zero ...
NettetLine Bundles on Super Riemann Surfaces . Abstract . We give the elements of a theory of line bundles, their classification, and their connec-tions on super Riemann surfaces. There are several salient departures from the classicalcase. For example, the dimension of the Picard group is not constant, and there is nonatural hermitian form on Pic. All compact Riemann surfaces are algebraic curves since they can be embedded into some . This follows from the Kodaira embedding theorem and the fact there exists a positive line bundle on any complex curve. Important examples of non-compact Riemann surfaces are provided by analytic continuation. Se mer In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. … Se mer • The complex plane C is the most basic Riemann surface. The map f(z) = z (the identity map) defines a chart for C, and {f} is an Se mer The existence of non-constant meromorphic functions can be used to show that any compact Riemann surface is a projective variety, i.e. can be given by polynomial equations … Se mer The geometric classification is reflected in maps between Riemann surfaces, as detailed in Liouville's theorem and the Little Picard theorem: maps from hyperbolic to parabolic to elliptic are easy, but maps from elliptic to parabolic or parabolic to hyperbolic are very … Se mer There are several equivalent definitions of a Riemann surface. 1. A Riemann surface X is a connected complex manifold Se mer As with any map between complex manifolds, a function f: M → N between two Riemann surfaces M and N is called holomorphic if … Se mer The set of all Riemann surfaces can be divided into three subsets: hyperbolic, parabolic and elliptic Riemann surfaces. Geometrically, these correspond to surfaces with … Se mer Nettet8. jul. 2024 · Anyway, if you are given a holomorphic line bundle π: E → X, a holomorphic section is a holomorphic map s: X → E such that π ∘ s = Id X. σ α = g α β ⋅ σ β. Now, fix any holomorphic section s of E, given locally on U α by holomorphic functions σ α. Then, you can identify holomorphic sections of E with meromorphic functions f ... lititz whiff roaster