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Configuration Spaces pp 1–39Cite as

Around the Tangent Cone Theorem

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Part of the book series: Springer INdAM Series ((SINDAMS,volume 14))

Abstract

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.

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Acknowledgements

I wish to thank Stefan Papadima for several useful conversations regarding this work, and also the referee, for a careful reading of the manuscript. This work was supported in part by National Security Agency grant H98230-13-1-0225.

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    Alexander I. Suciu

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  1. Alexander I. Suciu
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Correspondence to Alexander I. Suciu .

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Editors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Filippo Callegaro

  2. Department of Mathematics, University of Rochester, Rochester, USA

    Frederick Cohen

  3. Dipartimento di Matematica, Università di Roma La Sapienza, Roma, Italy

    Corrado De Concini

  4. Department of Mathematics, University of Bremen, Bremen, Germany

    Eva Maria Feichtner

  5. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Giovanni Gaiffi

  6. Dipartimento di Matematica, Università di Pisa, Pisa, Italy

    Mario Salvetti

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Suciu, A.I. (2016). Around the Tangent Cone Theorem. In: Callegaro, F., Cohen, F., De Concini, C., Feichtner, E., Gaiffi, G., Salvetti, M. (eds) Configuration Spaces. Springer INdAM Series, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-31580-5_1

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