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A q-algebraic function is an analytic function that is in the algebraic closure of the ring of polynomials. In this work we study the q-algebraic spaces (i.e. the ringed spaces that locally are isomorphic to the locus of zeros of a finite number of q-algebraic functions) and we prove, for instance, that any q-algebraic, compact, connected manifold of is homogeneous (in the q-algebraic sense).
To each isolated singularity of hypersurface of dimension , one associates the local fundamental group of the moduli space minus the discriminant locus, and a representation , where is the -homology group, with integer coefficient, of the "non singular fibre". Although in general it is very difficult to determine even a presentation of , we show that the image of can be fairly rather easily, by using some relations in a first approximative presentation of , in the case of polynomials...
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