Finite monodromy of Pochhammer equation

Haraoka, Yoshishige

doi:10.5802/aif.1417

Cited by 19 publications

(16 citation statements)

References 6 publications

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“…We start with a generalization of the well known normal forms of the Pochhammer tuples computed in Takano and Bannai (1976) (see also Haraoka, 1994) in the onedimensional case where…”

Section: Definition Of the Convolution Functormentioning

confidence: 99%

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mentioning

confidence: 99%

“…Perhaps the best-studied ordinary differential equations are the generalized hypergeometric differential equations (see Levelt, 1961;Beukers and Heckman, 1989;Sasai, 1992) and the Jordan-Pochhammer differential equations (see Pochhammer, 1870;Takano and Bannai, 1976;Haraoka, 1994) which are free from accessory parameters. We call the corresponding tuples Levelt triples respectively Jordan-Pochhammer tuples.…”

Section: Introductionmentioning

confidence: 99%

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An Algorithm of Katz and its Application to the Inverse Galois Problem

Dettweiler

Reiter

2000

Journal of Symbolic Computation

145

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In this paper we present a new and elementary approach for proving the main results of Katz (1996) using the Jordan-Pochhammer matrices of Takano and Bannai (1976) and Haraoka (1994). We find an explicit version of the middle convolution of Katz (1996) that connects certain tuples of matrices in linear groups. From this, Katz' existence algorithm for rigid tuples in linear groups can easily be deduced. It can further be shown that the convolution operation on tuples commutes with the braid group action.This yields a new approach in inverse Galois theory for realizing subgroups of linear groups regularly as Galois groups over Q. This approach is then applied to realize numerous series of classical groups regularly as Galois groups over Q.In the Appendix we treat an additive version of the convolution.

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“…We start with a generalization of the well known normal forms of the Pochhammer tuples computed in Takano and Bannai (1976) (see also Haraoka, 1994) in the onedimensional case where…”

Section: Definition Of the Convolution Functormentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Algorithm of Katz and its Application to the Inverse Galois Problem

Dettweiler

Reiter

2000

Journal of Symbolic Computation

145

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“…4.8 (cf. [27]). We remark that the lemma applies in many other contexts, e.g., for more general rigid local systems or motivic local systems whose Hodge numbers can be calculated (cf.…”

Section: Cyclic Coverings Of the Projective Line Branched Onmentioning

confidence: 99%

Vector bundles on curves coming from variation of Hodge structures

Catanese

Dettweiler

2016

Int. J. Math.

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Abstract. Fujita's second theorem for Kähler fibre spaces over a curve asserts that the direct image V of the relative dualizing sheaf splits as the direct sum V = A ⊕ Q, where A is ample and Q is unitary flat. We focus on our negative answer ([9]) to a question by Fujita: is V semiample?We give here an infinite series of counterexamples using hypergeometric integrals and we give a simple argument to show that the monodromy representation is infinite. Our counterexamples are surfaces of general type with positive index, explicitly given as abelian coverings with group (Z/n) 2 of a Del Pezzo surface of degree 5 (branched on a union of lines forming a bianticanonical divisor), and endowed with a semistable fibration with only 3 singular fibres.The simplest such surfaces are the three ball quotients considered in [3], fibred over a curve of genus 2, and with fibres of genus 4.These examples are a larger class than the ones corresponding to Shimura curves in the moduli space of Abelian varieties.

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“…we obtain the Pochhammer system (5.6) of rank n with Then we can construct an integral representation of solutions of the Pochhammer system, which has been already known [IKSY,H3], by applying our method to the above operation. First, we note the following fact.…”

Section: Pochhammer Systemmentioning

confidence: 99%

Integral Representations of Solutions of Differential Equations Free from Accessory Parameters

Haraoka

2002

Advances in Mathematics

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We show that every accessory parameter free system of differential equations of Okubo normal form has integral representation of solutions. The proof is constructive; we study the change of solutions under the operations}the extension and the restriction, which have been introduced by Yokoyama [Construction of systems of differential equations of Okubo normal form with rigid monodromy, preprint] in order to construct every such system of differential equations. Several examples are given. # 2002 Elsevier Science (USA)

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Finite monodromy of Pochhammer equation

Cited by 19 publications

References 6 publications

An Algorithm of Katz and its Application to the Inverse Galois Problem

An Algorithm of Katz and its Application to the Inverse Galois Problem

Vector bundles on curves coming from variation of Hodge structures

Integral Representations of Solutions of Differential Equations Free from Accessory Parameters

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