On a twisted de Rham complex
Copyright policy )On a twisted de Rham complex
We show that, given a projective regular function f on a smooth quasi-projective variety over C, the corresponding cohomology groups of the algebraic de Rham complex with twisted differential d-df and of the complex of algebraic forms with differential df have the same dimension (a result announced by Barannikov and Kontsevitch). We generalize the result to de Rham complexes with coefficients in a mixed Hodge Module.
AMS-LaTeX with amsart.sty. 15 pages
- Laurent Schwartz Center for Mathematics France
- École Polytechnique France
14D07, 14D05, 32G20, 32S40, Variation of Hodge structures (algebro-geometric aspects), 14D05, mixed Hodge module, 14D07, hypercohomology spaces, 32G20, Period matrices, variation of Hodge structure; degenerations, differential complex, 510, 14F40, Mathematics - Algebraic Geometry, de Rham complex, 32S40, 32C38, Structure of families (Picard-Lefschetz, monodromy, etc.), Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, vanishing cycle, FOS: Mathematics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Algebraic Geometry (math.AG), Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
14D07, 14D05, 32G20, 32S40, Variation of Hodge structures (algebro-geometric aspects), 14D05, mixed Hodge module, 14D07, hypercohomology spaces, 32G20, Period matrices, variation of Hodge structure; degenerations, differential complex, 510, 14F40, Mathematics - Algebraic Geometry, de Rham complex, 32S40, 32C38, Structure of families (Picard-Lefschetz, monodromy, etc.), Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, vanishing cycle, FOS: Mathematics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Algebraic Geometry (math.AG), Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
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