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HIGGS BUNDLES AND LOCAL SYSTEMS ON RIEMANN SURFACES
HIGGS BUNDLES LOCAL SYSTEMS RIEMANN SURFACES
2015/12/17
These notes are based on lectures given at the Third International School on Geometry and Physics at the Centre de Recerca Matem`atica in Barcelona, March 26–30, 2012. The aim ofthe School’s four lect...
DELIGNE PAIRINGS AND FAMILIES OF RANK ONE LOCAL SYSTEMS ON ALGEBRAIC CURVES
DELIGNE PAIRINGS LOCAL SYSTEMS ALGEBRAIC CURVES
2015/12/17
For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, ...
Character algebras of decorated SL_2(C)-local systems
Character algebras decorated SL_2(C)-local systems Geometric Topology
2011/9/13
Abstract: Let S be a path-connected, locally-compact CW-complex, and let M be a subcomplex with finitely-many components. A `decorated SL_2(C)-local system' is an SL_2(C)-local system on S, together w...
On the cohomology groups of local systems over Hilbert modular varieties via Higgs bundles
cohomology groups of local systems Hilbert modular varieties Higgs bundles
2010/12/3
Let X be a Hilbert modular variety and V a non-trivial local system over X. In this paper we study Deligne-Saito’s mixed Hodge structure (MHS) on the cohomology groups Hk(X, V) using the method of Hig...
Minimal models, formality and hard Lefschetz properties of solvmanifolds with local systems
solvmanifold Sullivan’s minimal model formality Hard Lefschetz property
2010/12/3
For a simply connected solvable Lie group G with a cocompact discrete subgroup , we consider the space of differential forms on the solvmanifold G/with values in certain flat bundl...