MONOMIALIZATION OF MORPHISMS FROM 3-FOLDS TO SURFACES

By KENNETH RODRIGUEZ

CONTENTS 1 INTRODUCTION 2 LOCAL MONOMIALIZATION 3 MONOMIALIZATION OF MORPHISMS IN LOW DIMENSIONS 4 AN OVERVIEW OF THE PROOF OF MONOMIALIZATION OF MORPHISMS FROM 3 FOLDS TO SURFACES 5 NOTATIONS 6 THE INVARIANT ? 7 THE INVARIANT ? UNDER QUADRATIC TRANSFORMS 8 PERMISSIBLE MONOIDAL TRANSFORMS CENTERED AT CURVES 9 POWER SERIES IN 2 VARIABLES 10 AR(X) 11 REDUCTION OF ? IN A SPECIAL CASE 12 REDUCTION OF ? IN A SECOND SPECIAL CASE 13 RESOLUTION 14 RESOLUTION 15 RESOLUTION 16 RESOLUTION 17 PROOF OF THE MAIN THEOREM 18 MONOMIALIZATION 19 TOROIDALIZATION 20 GLOSSARY OF NOTATIONS AND DE?NITIONS REFERENCES