Périodes évanescentes et (a,b)-modules monogènes
Bollettino dell'Unione Matematica Italiana (2009)
- Volume: 2, Issue: 3, page 651-697
- ISSN: 0392-4041
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topBarlet, Daniel. "Périodes évanescentes et (a,b)-modules monogènes." Bollettino dell'Unione Matematica Italiana 2.3 (2009): 651-697. <http://eudml.org/doc/290588>.
@article{Barlet2009,
abstract = {In order to describe the asymptotic behaviour of a vanishing period in the degeneration of a one parameter family of complex manifolds, we introduce and use a very simple algebraic structure encoding the corresponding filtered Gauss-Manin connection: regular geometric (a,b)-module generated (as left $\widetilde\{A\}$-modules) by one element. The idea is to use not the full Brieskorn module associated to the Gauss-Manin connection but the minimal (regular) filtered differential equation satisfied by the period integral we are interested in. We show that the Bernstein polynomial associated is quite simple to compute for such (a,b)-modules and give a precise description of the exponents which appears in the asymptotic expansion which avoids integral shifts. We show the efficiency of this tool on a couple of explicit computations in some classical (but not so easy) examples.},
author = {Barlet, Daniel},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {651-697},
publisher = {Unione Matematica Italiana},
title = {Périodes évanescentes et (a,b)-modules monogènes},
url = {http://eudml.org/doc/290588},
volume = {2},
year = {2009},
}
TY - JOUR
AU - Barlet, Daniel
TI - Périodes évanescentes et (a,b)-modules monogènes
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/10//
PB - Unione Matematica Italiana
VL - 2
IS - 3
SP - 651
EP - 697
AB - In order to describe the asymptotic behaviour of a vanishing period in the degeneration of a one parameter family of complex manifolds, we introduce and use a very simple algebraic structure encoding the corresponding filtered Gauss-Manin connection: regular geometric (a,b)-module generated (as left $\widetilde{A}$-modules) by one element. The idea is to use not the full Brieskorn module associated to the Gauss-Manin connection but the minimal (regular) filtered differential equation satisfied by the period integral we are interested in. We show that the Bernstein polynomial associated is quite simple to compute for such (a,b)-modules and give a precise description of the exponents which appears in the asymptotic expansion which avoids integral shifts. We show the efficiency of this tool on a couple of explicit computations in some classical (but not so easy) examples.
LA - eng
UR - http://eudml.org/doc/290588
ER -
References
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