Local isoformal deformation theory for meromorphic differential equations near an irregular singularity.

*(English)*Zbl 0668.34010
Deformation theory of algebras and structures and applications, Nato Adv. Study Inst., Castelvecchio-Pasoli/Italy 1986, Nato ASI Ser., Ser. C 247, 583-700 (1988).

[For the entire collection see Zbl 0654.00006.]

The paper, consisting of several lectures, is concerned with so-called isoformal deformations of meromorphic differential equations in the neighborhood of an irregular singularity. The authors construct a corresponding moduli space and show that it is the quotient of a complex affine space by an affine algebraic group. The theory is partly based upon deforming nilpotent matrices over rings. Other ingredients are the Stokes sheaf and cohomology of non-abelian sheaves of groups. Also some examples are discussed. A part of the results was announced in an earlier paper by the authors in Bull. Am. Math. Soc., New Ser. 12, 95-98 (1985; Zbl 0579.34005).

The paper, consisting of several lectures, is concerned with so-called isoformal deformations of meromorphic differential equations in the neighborhood of an irregular singularity. The authors construct a corresponding moduli space and show that it is the quotient of a complex affine space by an affine algebraic group. The theory is partly based upon deforming nilpotent matrices over rings. Other ingredients are the Stokes sheaf and cohomology of non-abelian sheaves of groups. Also some examples are discussed. A part of the results was announced in an earlier paper by the authors in Bull. Am. Math. Soc., New Ser. 12, 95-98 (1985; Zbl 0579.34005).

Reviewer: S.Kosarew

##### MSC:

34M35 | Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms |

32G13 | Complex-analytic moduli problems |

34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |