Period mapping via Brieskorn modules

Saito, Morihiko

doi:10.24033/bsmf.2162

Cited by 19 publications

(10 citation statements)

References 15 publications

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“…This improves a slightly weaker result (finite-to-one) in [Sa2]. It is an infinitesimal Torelli type result.…”

Section: Period Maps and Torelli Type Problemssupporting

confidence: 69%

\mu -constant monodromy groups and marked singularities

Hertling¹

2011

Ann. inst. Fourier

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µ-constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a fixed singularity is studied. It consists of automorphisms of the Milnor lattice which respect not only the intersection form, but also the Seifert form and the monodromy. We conjecture that it contains all such automorphisms, modulo ± id. Second, marked singularities are defined and global moduli spaces for right equivalence classes of them are established. The conjecture on the group would imply that these moduli spaces are connected. The relation with Torelli type problems is discussed and a new global Torelli type conjecture for marked singularities is formulated. All conjectures are proved for the simple and 22 of the 28 exceptional singularities.

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“…This improves a slightly weaker result (finite-to-one) in [Sa2]. It is an infinitesimal Torelli type result.…”

Section: Period Maps and Torelli Type Problemssupporting

confidence: 69%

\mu -constant monodromy groups and marked singularities

Hertling¹

2011

Ann. inst. Fourier

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“…(U), df 1B) has cohomology in degree n only, hence and (see also [16] where this is stated for cohomologically tame polynomials). [52] and [44], see also [14]), hence, by [52] [56] and M. Saito [58], [60], as adapted to this situation in [50]. 3.a.…”

Section: One Deduces Thatmentioning

confidence: 99%

“…volume forms. In the singularity case, the minimal exponent has multiplicity one [60], so such a primitive homogeneous section is essentially unique, if it exists. In fact, any volume form gives rise to such a primitive homogeneous section.…”

mentioning

confidence: 99%

Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)

Douai¹,

Sabbah²

2003

Annales De L’institut Fourier

154

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“…A better invariant for Torelli type questions is the Brieskorn lattice H 00 0 = n+1 C n+1 ;0 = df^d n,1 C n+1 ;0 [Br]. M. Saito showed that it varies holomorphically within the -constant stratum, and that it is sensitive to all of the analytic moduli [SM1] [SM2]. So it satisfies some infinitesimal Torelli theorem.…”

Section: Introductionmentioning

confidence: 99%

“…Other, more detailed expositions can be found in [He1] [Ka] (Sects. 1, 2 in [Ka], see [SM2] for a critical discussion of the statements in the following chapters of [Ka]). Just as the Brieskorn lattice can be seen as an extension of the mixed Hodge structure, there is an extension of the polarizing form S to the Gauß-Manin connection.…”

Section: Introductionmentioning

confidence: 99%

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Hertling¹

1999

Compositio Mathematica

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Abstract. Classifying spaces and moduli spaces are constructed for two invariants of isolated hypersurface singularities, for the polarized mixed Hodge structure on the middle cohomology of the Milnor fibre, and for the Brieskorn lattice as a subspace of the Gauß-Manin connection. The relations between them, period mappings for -constant families of singularities, and Torelli theorems are discussed.Mathematics Subject Classifications (1991): 32S25, 32S35, 14D07.

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Period mapping via Brieskorn modules

Cited by 19 publications

References 15 publications

\mu -constant monodromy groups and marked singularities

\mu -constant monodromy groups and marked singularities

Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)

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