scholarly journals On Determinant Line Bundles

1987 ◽  
Author(s):  
DANIEL S. FREED
Keyword(s):  
Line Bundles ◽  
Determinant Line Bundles

scholarly journals Remarks on Determinant Line Bundles, Chern-Simons Forms and Invariants

2002 ◽  
Vol 91 (1) ◽  
pp. 5 ◽  
Author(s):  
Johan L. Dupont ◽  
Flemming Lindblad Johansen
Keyword(s):  
Line Bundle ◽  
Line Bundles ◽  
Manifolds With Boundary ◽  
Principal Bundles ◽  
Determinant Line Bundles ◽  
Chern Simons ◽  
Determinant Line Bundle

We study generalized determinant line bundles for families of principal bundles and connections. We explore the connections of this line bundle and give conditions for the uniqueness of such. Furthermore we construct for families of bundles and connections over manifolds with boundary, a generalized Chern-Simons invariant as a section of a determinant line bundle.

scholarly journals On the S-fundamental group scheme. II

2012 ◽  
Vol 11 (4) ◽  
pp. 835-854 ◽  
Author(s):  
Adrian Langer
Keyword(s):  
Fundamental Group ◽  
Abelian Variety ◽  
Vector Bundles ◽  
Group Scheme ◽  
Line Bundles ◽  
Fundamental Groups ◽  
Determinant Line Bundles

AbstractThe S-fundamental group scheme is the group scheme corresponding to the Tannaka category of numerically flat vector bundles. We use determinant line bundles to prove that the S-fundamental group of a product of two complete varieties is a product of their S-fundamental groups as conjectured by Mehta and the author. We also compute the abelian part of the S-fundamental group scheme and the S-fundamental group scheme of an abelian variety or a variety with trivial étale fundamental group.

scholarly journals Refined Verlinde formulas for Hilbert schemes of points and moduli spaces of sheaves on K3 surfaces

2020 ◽  
Vol Volume 4 ◽  
Author(s):  
Lothar Göttsche
Keyword(s):  
Moduli Spaces ◽  
Generating Functions ◽  
K3 Surfaces ◽  
Line Bundles ◽  
Hilbert Schemes ◽  
Moduli Spaces Of Sheaves ◽  
Elliptic Genera ◽  
Determinant Line Bundles

We compute generating functions for elliptic genera with values in line bundles on Hilbert schemes of points on surfaces. As an application we also compute generating functions for elliptic genera with values in determinant line bundles on moduli spaces of sheaves on K3 surfaces.

scholarly journals DETERMINANT LINE BUNDLES AND TOPOLOGICAL INVARIANTS OF HYPERBOLIC GEOMETRY

2002 ◽  
Vol 17 (06n07) ◽  
pp. 951-955
Author(s):  
ANDREI A. BYTSENKO
Keyword(s):  
Dirac Operator ◽  
Hyperbolic Geometry ◽  
Hyperbolic Manifolds ◽  
Line Bundles ◽  
Topological Invariants ◽  
Twisted Dirac Operator ◽  
Determinant Line Bundles

Some remarks on determinant line bundles and topological invariants are given. The index of the twisted Dirac operator acting on real hyperbolic manifolds is computed. We briefly discuss physical applications of results.

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