POLYNOMIALS AND VANISHING CYCLES

By JESSICA RAMIREZ

CONTENTS REGULARITY CONDITIONS AT IN?NITY ATYPICAL VALUES ?-REGULARITY AND T-REGULARITY THE MALGRANGE CONDITION DETECTING ATYPICAL VALUES VIA SINGULARITIES AT IN?NITY POLAR CURVES THE CASE OF ISOLATED SINGULARITIES TWO VARIABLES LOCAL AND GLOBAL ?BRATIONS FIBRATIONS A GLOBAL BOUQUET THEOREM COMPUTING THE NUMBER OF VANISHING CYCLES FAMILIES OF COMPLEX POLYNOMIALS DEFORMATIONS TO GENERAL HYPERSURFACES SEMI-CONTINUITY OF NUMBERS LOCAL CONSERVATION TOPOLOGY OF A FAMILY AND CONTACT STRUCTURES TOPOLOGICAL EQUIVALENCE OF POLYNOMIALS VARIATION OF THE MONODROMY IN FAMILIES CONTACT STRUCTURES AT IN?NITY POLAR INVARIANTS AND TOPOLOGY OF AF?NE VARIETIES THE LEFSCHETZ SLICING PRINCIPLE GLOBAL EULER OBSTRUCTION AF?NE POLAR VARIETIES AND MACPHERSON CYCLES RELATIVE POLAR CURVES AND FAMILIES OF AF?NE HYPERSURFACES LOCAL AND GLOBAL RELATIVE POLAR CURVES ASYMPTOTIC EQUISINGULARITY PLÜCKER FORMULA FOR AF?NE HYPERSURFACES CURVATURE LOSS AT IN?NITY AND THE GAUSS–BONNET DEFECT MONODROMY OF POLYNOMIALS MODELS OF ?BRES AND A GLOBAL GEOMETRIC MONODROMY RELATIVE MONODROMY AND ZETA FUNCTION THE S-MONODROMY AND BOUNDARY SINGULARITIES TOPOLOGY OF MEROMORPHIC FUNCTIONS SINGULARITIES OF MEROMORPHIC FUNCTIONS VANISHING HOMOLOGY AND SINGULARITIES FIBRES AND AF?NE HYPERSURFACE COMPLEMENTS MONODROMY OF MEROMORPHIC FUNCTIONS SLICING BY PENCILS OF HYPERSURFACES 10 1 RELATIVE CONNECTIVITY OF PENCILS 10 2 SECOND LEFSCHETZ HYPERPLANE THEOREM 10 3 VANISHING CYCLES OF POLYNOMIALS, REVISITED HIGHER ZARISKI–LEFSCHETZ THEOREMS 11 1 HOMOTOPY VARIATION MAPS 11 2 GENERAL ZARISKI–LEFSCHETZ THEOREM FOR NONGENERIC PENCILS 11 3 SPECIALIZATIONS OF THE ZARISKI–LEFSCHETZ THEOREM BIBLIOGRAPHY