Topological and Hodge L-classes of singular covering spaces and varieties with trivial canonical class
The signature of closed oriented manifolds is well-known to be multiplicative under finite covers. This fails for Poincaré complexes as examples of C. T. C. Wall show. We establish the multiplicativity of the signature, and more generally, the topological L-class, for closed oriented stratified pse...
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| Main Author: | |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
[April 2019]
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| In: |
Geometriae dedicata
Year: 2018, Volume: 199, Issue: 1, Pages: 189-224 |
| ISSN: | 1572-9168 |
| DOI: | 10.1007/s10711-018-0345-2 |
| Online Access: | Verlag, Volltext: https://doi.org/10.1007/s10711-018-0345-2
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| Author Notes: | Markus Banagl |
MARC
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| 520 | |a The signature of closed oriented manifolds is well-known to be multiplicative under finite covers. This fails for Poincaré complexes as examples of C. T. C. Wall show. We establish the multiplicativity of the signature, and more generally, the topological L-class, for closed oriented stratified pseudomanifolds that can be equipped with a middle-perverse Verdier self-dual complex of sheaves, determined by Lagrangian sheaves along strata of odd codimension. This class of spaces, called L-pseudomanifolds, contains all Witt spaces and thus all pure-dimensional complex algebraic varieties. We apply this result in proving the Brasselet-Schürmann-Yokura conjecture for normal complex projective 3-folds with at most canonical singularities, trivial canonical class and positive irregularity. The conjecture asserts the equality of topological and Hodge L-class for compact complex algebraic rational homology manifolds. | ||
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| 650 | 4 | |a 57R20 | |
| 650 | 4 | |a Calabi-Yau varieties | |
| 650 | 4 | |a Canonical singularities | |
| 650 | 4 | |a Characteristic classes | |
| 650 | 4 | |a Hodge theory | |
| 650 | 4 | |a Intersection homology | |
| 650 | 4 | |a Perverse sheaves | |
| 650 | 4 | |a Pseudomanifolds | |
| 650 | 4 | |a Signature | |
| 650 | 4 | |a Stratified spaces | |
| 650 | 4 | |a Varieties of Kodaira dimension zero | |
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