scholarly journals Determinant bundles, boundaries, and surgery

2004 ◽  
Vol 52 (1) ◽  
pp. 28-43 ◽  
Author(s):  
Ulrich Bunke ◽  
Jinsung Park
Keyword(s):  
Determinant Bundles

scholarly journals SOME INDEX FORMULAE ON THE MODULI SPACE OF STABLE PARABOLIC VECTOR BUNDLES

2013 ◽  
Vol 94 (1) ◽  
pp. 1-37
Author(s):  
PIERRE ALBIN ◽  
FRÉDÉRIC ROCHON
Keyword(s):  
Moduli Space ◽  
Vector Bundles ◽  
Index Theorem ◽  
Chern Classes ◽  
Chern Characters ◽  
Natural Vector ◽  
Parabolic Structure ◽  
Determinant Bundles ◽  
Natural Families

AbstractWe study natural families of $\bar {\partial } $-operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulae for the Chern characters of the associated index bundles. The contributions from the cusps are explicitly expressed in terms of the Chern characters of natural vector bundles related to the parabolic structure. We show that our result implies formulae for the Chern classes of the associated determinant bundles consistent with a result of Takhtajan and Zograf.

Analytic torsion and holomorphic determinant bundles

1988 ◽  
Vol 115 (2) ◽  
pp. 301-351 ◽  
Author(s):  
Jean-Michel Bismut ◽  
Henri Gillet ◽  
Christophe Soul�
Keyword(s):  
Analytic Torsion ◽  
Determinant Bundles

scholarly journals ABELIAN CONFORMAL FIELD THEORY AND DETERMINANT BUNDLES

2007 ◽  
Vol 18 (08) ◽  
pp. 919-993 ◽  
Author(s):  
JØRGEN ELLEGAARD ANDERSEN ◽  
KENJI UENO
Keyword(s):  
Field Theories ◽  
Line Bundles ◽  
Conformal Field Theories ◽  
Nodal Curves ◽  
Conformal Field ◽  
Families Of Curves ◽  
Holomorphic Sections ◽  
Explicit Relation ◽  
Holomorphic Line Bundles ◽  
Determinant Bundles

Following [10], we study a so-called bc-ghost system of zero conformal dimension from the viewpoint of [14, 16]. We show that the ghost vacua construction results in holomorphic line bundles with connections over holomorphic families of curves. We prove that the curvature of these connections are up to a scale the same as the curvature of the connections constructed in [14, 16]. We study the sewing construction for nodal curves and its explicit relation to the constructed connections. Finally we construct preferred holomorphic sections of these line bundles and analyze their behaviour near nodal curves. These results are used in [4] to construct modular functors form the conformal field theories given in [14, 16] by twisting with an appropriate factional power of this Abelian theory.

scholarly journals Curvature on determinant bundles and first Chern forms

2003 ◽  
Vol 45 (3-4) ◽  
pp. 393-429 ◽  
Author(s):  
Sylvie Paycha ◽  
Steven Rosenberg
Keyword(s):  
Determinant Bundles ◽  
Chern Forms
Sign in / Sign up

Export Citation Format

Share Document