Irregularity of an analogue of the Gauss-Manin systems

Céline Roucairol

Bulletin de la Société Mathématique de France (2006)

  • Volume: 134, Issue: 2, page 269-286
  • ISSN: 0037-9484

Abstract

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In 𝒟 -modules theory, Gauss-Manin systems are defined by the direct image of the structure sheaf 𝒪 by a morphism. A major theorem says that these systems have only regular singularities. This paper examines the irregularity of an analogue of the Gauss-Manin systems. It consists in the direct image complex f + ( 𝒪 e g ) of a 𝒟 -module twisted by the exponential of a polynomial g by another polynomial  f , where f and g are two polynomials in two variables. The analogue of the Gauss-Manin systems can have irregular singularities (at finite distance and at infinity). We express an invariant associated with the irregularity of these systems at  c ∈ ℙ 1 by the geometry of the map ( f , g ) .

How to cite

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Roucairol, Céline. "Irregularity of an analogue of the Gauss-Manin systems." Bulletin de la Société Mathématique de France 134.2 (2006): 269-286. <http://eudml.org/doc/272495>.

@article{Roucairol2006,
abstract = {In $\mathcal \{D\}$-modules theory, Gauss-Manin systems are defined by the direct image of the structure sheaf $\mathcal \{O\}$ by a morphism. A major theorem says that these systems have only regular singularities. This paper examines the irregularity of an analogue of the Gauss-Manin systems. It consists in the direct image complex $f_+(\mathcal \{O\}\hspace\{0.55542pt\}\{\rm e\hspace\{0.55542pt\}\}^g)$ of a $\mathcal \{D\}$-module twisted by the exponential of a polynomial $g$ by another polynomial $f$, where $f$ and $g$ are two polynomials in two variables. The analogue of the Gauss-Manin systems can have irregular singularities (at finite distance and at infinity). We express an invariant associated with the irregularity of these systems at $c\in \mathbb \{P\}^1$ by the geometry of the map $(f,g)$.},
author = {Roucairol, Céline},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Gauss-Manin connection; irregularity complex; direct image; elementary $\mathcal \{D\}$-modules},
language = {eng},
number = {2},
pages = {269-286},
publisher = {Société mathématique de France},
title = {Irregularity of an analogue of the Gauss-Manin systems},
url = {http://eudml.org/doc/272495},
volume = {134},
year = {2006},
}

TY - JOUR
AU - Roucairol, Céline
TI - Irregularity of an analogue of the Gauss-Manin systems
JO - Bulletin de la Société Mathématique de France
PY - 2006
PB - Société mathématique de France
VL - 134
IS - 2
SP - 269
EP - 286
AB - In $\mathcal {D}$-modules theory, Gauss-Manin systems are defined by the direct image of the structure sheaf $\mathcal {O}$ by a morphism. A major theorem says that these systems have only regular singularities. This paper examines the irregularity of an analogue of the Gauss-Manin systems. It consists in the direct image complex $f_+(\mathcal {O}\hspace{0.55542pt}{\rm e\hspace{0.55542pt}}^g)$ of a $\mathcal {D}$-module twisted by the exponential of a polynomial $g$ by another polynomial $f$, where $f$ and $g$ are two polynomials in two variables. The analogue of the Gauss-Manin systems can have irregular singularities (at finite distance and at infinity). We express an invariant associated with the irregularity of these systems at $c\in \mathbb {P}^1$ by the geometry of the map $(f,g)$.
LA - eng
KW - Gauss-Manin connection; irregularity complex; direct image; elementary $\mathcal {D}$-modules
UR - http://eudml.org/doc/272495
ER -

References

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  10. [10] —, « Le théorème de positivité, le théorème de comparaison, le théorème d’existence de Riemann », Séminaires et Congrès8 (2004), p. 165–307. Zbl1082.32006
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