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Monodromy of a family of hypersurfaces

Vincenzo Di Gennaro, Davide Franco (2009)

Annales scientifiques de l'École Normale Supérieure

Let Y be an ( m + 1 ) -dimensional irreducible smooth complex projective variety embedded in a projective space. Let Z be a closed subscheme of Y , and δ be a positive integer such that Z , Y ( δ ) is generated by global sections. Fix an integer d δ + 1 , and assume the general divisor X | H 0 ( Y , Z , Y ( d ) ) | is smooth. Denote by H m ( X ; ) Z van the quotient of H m ( X ; ) by the cohomology of Y and also by the cycle classes of the irreducible components of dimension m of Z . In the present paper we prove that the monodromy representation on H m ( X ; ) Z van for the family of smooth...

Monotone Hurwitz Numbers and the HCIZ Integral

I. P. Goulden, Mathieu Guay-Paquet, Jonathan Novak (2014)

Annales mathématiques Blaise Pascal

In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of z = 0 . Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.

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