Get Nonabelian Jacobian of Projective Surfaces: Geometry and PDF

By Igor Reider

ISBN-10: 3642356613

ISBN-13: 9783642356612

The Jacobian of a delicate projective curve is definitely the most notable and lovely items in algebraic geometry. This paintings is an try and enhance an identical concept for tender projective surfaces - a conception of the nonabelian Jacobian of gentle projective surfaces. similar to its classical counterpart, our nonabelian Jacobian pertains to vector bundles (of rank 2) on a floor in addition to its Hilbert scheme of issues. however it additionally comes outfitted with the adaptation of Hodge-like buildings, which produces a sheaf of reductive Lie algebras clearly hooked up to our Jacobian. This constitutes a nonabelian analogue of the (abelian) Lie algebra constitution of the classical Jacobian. this option clearly relates geometry of surfaces with the illustration idea of reductive Lie algebras/groups. This work’s major concentration is on delivering an in-depth examine of assorted points of this relation. It provides a considerable physique of facts that the sheaf of Lie algebras at the nonabelian Jacobian is a good software for utilizing the illustration concept to systematically tackle numerous algebro-geometric difficulties. It additionally exhibits how you can build new invariants of illustration theoretic starting place on gentle projective surfaces.

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