Nonabelian Jacobian of Projective Surfaces: Geometry and Representation Theory (Lecture Notes in Mathematics)
English | 235 pages | ISBN-10: 3642356613 | PDF | 4,06 MB
The Jacobian of a smooth projective curve is undoubtedly one of the most remarkable and be
autiful objects in algebraic geometry. This work is an attempt to develop an analogous theory for
smooth projective surfaces - a theory of the nonabe
lian Jacobian of smooth projective surfaces. Just like its classical counterpart, our nonabe
lian Jacobian relates to vector bundles (of rank 2) on a surface as well as its Hilbe
rt scheme of points. But it also comes equipped with the variation of Hodge-like structures, which produces a sheaf of reductive Lie algebras naturally attached to our Jacobian.