"The Jacobian of a smooth projective curve is undoubtedly one of the most remarkable and beautiful objects in algebraic geometry. This work is an attempt to develop an analogous theory for smooth projective surfaces - a theory of the nonabelian Jacobian of smooth projective surfaces. Just like its classical counterpart, our nonabelian Jacobian relates to vector bundles (of rank 2) on a surface as well as its Hilbert 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. This constitutes a nonabelian analogue of the (abelian) Lie algebra structure of the classical Jacobian. This feature naturally relates geometry of surfaces with the representation theory of reductive Lie algebras/groups. This work's main focus is on providing an in-depth study of various aspects of this relation. It presents a substantial body of evidence that the sheaf of Lie algebras on the nonabelian Jacobian is an efficient tool for using the representation theory to systematically address various algebro-geometric problems. It also shows how to construct new invariantsof representation theoretic origin on smooth projective surfaces."

"Nonabelian Jacobian of projective surfaces : geometry and representation theory"@en
"Nonabelian Jacobian of projective surfaces : geometry and representation theory"
"Nonabelian Jacobian of Projective Surfaces Geometry and Representation Theory"
"Nonabelien Jacobian of projective surfaces geometry and representation theory"
"Nonabelien Jacobian of projective surfaces : geometry and representation theory"
"Nonabelian Jacobian of projective surfaces geometry and representation theory"