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2 results

  • Laurent polynomials, GKZ-hypergeometric systems and mixed Hodge modules

  • Part of
  • Thomas Reichelt
  • Journal:
    Compositio Mathematica / Volume 150 / Issue 6 / June 2014
    Published online by Cambridge University Press:
    24 April 2014, pp. 911-941
    Print publication:
    June 2014
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  • We endow certain GKZ-hypergeometric systems with a natural structure of a mixed Hodge module, which is compatible with the mixed Hodge module structure on the Gauß–Manin system of an associated family of Laurent polynomials. As an application we show that the underlying perverse sheaf of a GKZ-system with rational parameter has quasi-unipotent local monodromy.

  • Linear free divisors and Frobenius manifolds

  • Part of
  • Ignacio de Gregorio, David Mond, Christian Sevenheck
  • Journal:
    Compositio Mathematica / Volume 145 / Issue 5 / September 2009
    Published online by Cambridge University Press:
    23 October 2009, pp. 1305-1350
    Print publication:
    September 2009
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  • We study linear functions on fibrations whose central fibre is a linear free divisor. We analyse the Gauß–Manin system associated to these functions, and prove the existence of a primitive and homogenous form. As a consequence, we show that the base space of the semi-universal unfolding of such a function carries a Frobenius manifold structure.