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Infinitesimal invariant and Massey products

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Abstract

In this work, we study the Griffiths infinitesimal invariant of the curve in the jacobian using secondary cohomology maps. In order to do this, we construct a special differential graded algebra \({\mathcal{A}}\) , quite similar to the Kodaira–Spencer algebra and we define a natural triple Massey product on it. This allows us to give a description of the infinitesimal invariant in terms of Massey products and to study the formality of \({\mathcal{A}}\) .

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References

  1. Ceresa G.: C is not algebraically equivalent to C −. Ann. Math. 117, 285–291 (1983)

    Article  MathSciNet  Google Scholar 

  2. Collino A., Pirola G.: The Griffiths infinitesimal invariant for curve in its Jacobian. Duke Math. J. 78, 59–88 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  3. Deligne P., Griffiths P., Morgan J., Sullivan D.: Real homotopy theory of Kaler manifolds. Invent. Math. 29, 245–274 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  4. Felix, Y., Halperin, S., Thomas, J.C.: Rational Homotopy Theory, GTM, vol. 205. Springer, Heidelberg (2000)

  5. Green M.: Griffiths’ infinitesimal invariant and the Abel–Jacobi map. J. Differ. Geom. 29, 545–555 (1989)

    MATH  Google Scholar 

  6. Green, M., Murre, J., Voisin, C.: Algebraic Cycles and Hodge Theory (Torino, Italy). Lecture Notes in Mathematics, vol. 1594, pp. 1–92. Springer, Berlin (1993)

  7. Griffiths P., Harris P.: Infinitesimal variation of Hodge structures (II): infinitesimal invariant of Hodge classes. Comp. Math. 50, 207–265 (1983)

    MATH  MathSciNet  Google Scholar 

  8. Griffiths P.: Infinitesimal variation of Hodge structures (III): determinantal varieties and the infinitesimal invariant of normal functions. Comp. Math. 50, 267–324 (1983)

    MATH  Google Scholar 

  9. Griffiths P., Morgan J.: Rational homotopy theory and differential forms. Birkehauser, Boston (1981)

    MATH  Google Scholar 

  10. Harris B.: Harmonic volumes. Acta Math. 150, 91–123 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  11. Pirola G., Rizzi C.: Infinitesimal invariant and vector bundles. Nagoya Math. J. 186, 95–118 (2007)

    MATH  MathSciNet  Google Scholar 

  12. Sullivan D.: Infinitesimal computation in topology. Inst. Hautes Etud. Sci. Publ. Math. 47, 269–331 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  13. Voisin, C.: Variations of Hodge Structure and Algebraic Cycles. In: Proceedings of International Congress of Mathematics, vols. 1, 2, pp. 706–715 (1994)

  14. Voisin C.: Une remarque sur l’invariant infinitesimal des functions normal. C. R. Acad. Sci. Paris Ser. I 307, 157–174 (1988)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica F. Brioschi, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    Cecilia Rizzi

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  1. Cecilia Rizzi
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Correspondence to Cecilia Rizzi.

Additional information

This work has been partially supported by: (1) PRIN 2005: “Spazi di moduli e teoria di Lie”; (2) Indam (Gnsaga); (3) Far 2006 (PV): “Varietà algebriche, calcolo algebrico, grafi orientati e topologici”. The author was also partially supported by a scholarship of Politecnico di Milano.

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Rizzi, C. Infinitesimal invariant and Massey products. manuscripta math. 127, 235–248 (2008). https://doi.org/10.1007/s00229-008-0207-6

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  • DOI: https://doi.org/10.1007/s00229-008-0207-6

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