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A twistor approach to the Kontsevich complexes

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Abstract

We study the V-filtration of the mixed twistor \(\mathcal {D}\)-modules associated to algebraic meromorphic functions. We prove that their relative de Rham complexes are quasi-isomorphic to the family of Kontsevich complexes. It reveals a generalized Hodge theoretic meaning of Kontsevich complexes. On the basis of the quasi-isomorphism, we revisit the results on the Kontsevich complexes due to H. Esnault, M. Kontsevich, C. Sabbah, M. Saito and J.-D. Yu from a viewpoint of mixed twistor \(\mathcal {D}\)-modules.

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References

  1. Esnault, H., Sabbah, C., Yu, J.-D.: \(E_1\)-degeneration of the irregular Hodge filtration, (with an appendix by M. Saito), J. Rein. Angew. Math. (2015). https://doi.org/10.1515/crelle-2014-0118

  2. Kashiwara, M.: \(D\)-Modules and Microlocal Calculus, Translations of Mathematical Monographs, 217. American Mathematical Society, Providence (2003)

    Google Scholar 

  3. Katzarkov, L., Kontsevich, M., Pantev, T.: Bogomolov–Tian–Todorov theorems for Landau–Ginzburg models. J. Differ. Geom. 105(1), 55–117 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Mochizuki, T.: Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor \(D\)-Modules I, II. Memoirs of AMS, vol. 185. American Mathematical Society, Washington (2007)

  5. Mochizuki, T.: Wild Harmonic Bundles and Wild Pure Twistor \(D\)-Modules, Astérisque 340. Société Mathématique de France, Paris (2011)

  6. Mochizuki, T.: Harmonic bundles and Toda lattices with opposite sign II. Commun. Math. Phys. 328, 1159–1198 (2014). https://doi.org/10.1007/s00220-014-1994-0

    Article  MathSciNet  MATH  Google Scholar 

  7. Mochizuki, T.: Mixed twistor \(D\)-modules. Lecture Notes in Mathematics 2125. Springer (2015)

  8. Sabbah, C.: Polarizable twistor \(D\)-modules. Astérisque 300, 1 (2005)

    MathSciNet  MATH  Google Scholar 

  9. Sabbah, C.: Wild twistor \(D\)-modules. In: Miwa, T., Matsuo, A., Nakashima, T., Saito, Y. (eds.) Algebraic Analysis and Around, Advanced Studies in Pure Mathematics, vol. 54, pp. 293–353. Mathematical Society of Japan, Tokyo (2009)

    Google Scholar 

  10. Sabbah, C., Yu, J.-D.: On the irregular Hodge filtration of exponentially twisted mixed Hodge modules. Forum Math. Sigma 3, 71 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  11. Saito, M.: Modules de Hodge polarisables. Publ. RIMS 24, 849–995 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  12. Saito, M.: Mixed Hodge modules. Publ. RIMS 26, 221–333 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  13. Yu, J.-D.: Irregular Hodge filtration on twisted de Rham cohomology. Manuscr. Math. 144(12), 99–133 (2014)

    Article  MathSciNet  MATH  Google Scholar 

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  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Takuro Mochizuki

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  1. Takuro Mochizuki
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Correspondence to Takuro Mochizuki.

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Mochizuki, T. A twistor approach to the Kontsevich complexes. manuscripta math. 157, 193–231 (2018). https://doi.org/10.1007/s00229-017-0989-5

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  • DOI: https://doi.org/10.1007/s00229-017-0989-5

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