Analytic Functions and Morse Theory.- Normal Forms of Functions.- Algebraic Topology of Manifolds.- Topology and Monodromy of Functions.- Integrals along Vanishing Cycles.- Vector Fields and Abelian Integrals.- Hodge Structures and …
Analytic Functions and Morse Theory.- Normal Forms of Functions.- Algebraic Topology of Manifolds.- Topology and Monodromy of Functions.- Integrals along Vanishing Cycles.- Vector Fields and Abelian Integrals.- Hodge Structures and Period Map.- Linear Differential Systems.- Holomorphic Foliations. Local Theory.- Holomorphic Foliations. Global Aspects.- The Galois Theory.- Hypergeometric Functions.
In singularity theory and algebraic geometry the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem an
In singularity theory and algebraic geometry the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem an
The authors prove the 1990 conjecture of Guralnick and Thompson on composition factors of monodromy groups. Using Riemann's existence theorem, the conjecture translates into a problem on primitive permutation groups. …
The authors prove the 1990 conjecture of Guralnick and Thompson on composition factors of monodromy groups. Using Riemann's existence theorem, the conjecture translates into a problem on primitive permutation groups. This group theoretic problem had been reduced to a question about actions of classical groups on subspaces of their natural modules. The key ingredients in the present proof are the authors' earlier fixed point ratio estimates for such actions and a result of Scott on the generation of linear groups.
Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsKay Magaard∗
Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsKay Magaard∗
In [12], we show that 3 of the 14 hypergeometric monodromy groups associated to Calabi-Yau threefolds, are arithmetic. Brav-Thomas (in [3]) show that 7 of the remaining 11, are thin. …
In [12], we show that 3 of the 14 hypergeometric monodromy groups associated to Calabi-Yau threefolds, are arithmetic. Brav-Thomas (in [3]) show that 7 of the remaining 11, are thin. In this article, we settle the arithmeticity problem for the 14 monodromy groups, by showing that, the remaining 4 are arithmetic.
The monodromy conjecture is a mysterious open problem in singularity theory. Its original version relates arithmetic and topological/geometric properties of a multivariate polynomial $f$ over the integers, more precisely, poles …
The monodromy conjecture is a mysterious open problem in singularity theory. Its original version relates arithmetic and topological/geometric properties of a multivariate polynomial $f$ over the integers, more precisely, poles of the $p$-adic Igusa zeta function of $f$ should induce monodromy eigenvalues of $f$. The case of interest is when the zero set of $f$ has singular points. We first present some history and motivation. Then we expose a proof in the case of two variables, and partial results in higher dimension, together with geometric theorems of independent interest inspired by the conjecture. We conclude with several possible generalizations.