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Progress on Syzygies of Algebraic Curves

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Moduli of Curves

Part of the book series: Lecture Notes of the Unione Matematica Italiana ((UMILN,volume 21))

Abstract

These notes discuss recent advances on syzygies on algebraic curves, especially concerning the Green, the Prym-Green and the Green-Lazarsfeld Secant Conjectures. The methods used are largely geometric and variational, with a special emphasis on examples and explicit calculations. The notes are based on series of lectures given in Daejeon (March 2013), Rome (November–December 2015) and Guanajuato (February 2016).

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Notes

  1. 1.

    Sylvester is responsible for a remarkable number of standard mathematical terms like matrix, discriminant, minor, Jacobian, Hessian, invariant, covariant and many others. Some of his other terms have not stuck, for instance his derogatory matrices, that is, matrices whose characteristic polynomial differs from the minimal polynomial are all but forgotten today.

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Authors and Affiliations

  1. Humboldt-Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, 10099, Berlin, Germany

    Gavril Farkas

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  1. Gavril Farkas
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Editors and Affiliations

  1. CIMAT, Guanajuato, Mexico

    Leticia Brambila Paz

  2. Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy

    Ciro Ciliberto

  3. Instituto Nacional de Matemática Pura, Rio de Janeiro, Brazil

    Eduardo Esteves

  4. Dipartimento di Matematica, Università di Roma Tre, Roma, Italy

    Margarida Melo

  5. Collège de France, Paris, France

    Claire Voisin

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Farkas, G. (2017). Progress on Syzygies of Algebraic Curves. In: Brambila Paz, L., Ciliberto, C., Esteves, E., Melo, M., Voisin, C. (eds) Moduli of Curves. Lecture Notes of the Unione Matematica Italiana, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-319-59486-6_4

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