Flattenings of projective curves, singularities of Schubert stratifications of Grassmannians and flag varieties, and bifurcations of Weierstrass points of algebraic curves

Abstract

CONTENTS Introduction 1. Singularities of Schubert cells of flag varieties 2. Cascades of projective curves 3. Stabilization of flattenings: projection, trace and duality 4. Infinitesimal transformations that preserve flattenings 5. Simple flattenings 6. Singularities of the bifurcation sets of generic three-parameter families 7. Integrable distributions on finite-dimensional manifolds 8. An integrable distribution in the space of flags of functions 9. The finite determinacy and versality theorems 10. Singularities of the bifurcation sets of the degree of oscillation 11. Bifurcations of Weierstrass points and ramification points of linear series References