Balanced Normal Cones and Fulton-MacPherson's Intersection Theory

Balanced Normal Cones and Fulton-macpherson’s Intersection Theory

Let X be a subscheme of a reduced scheme Y. Then Y has a flat degeneration to the normal cone CXY of X, and this degeneration plays a key step in Fulton and MacPherson’s “basic construction” in intersection theory. The intersection product has a canonical refinement as a sum over the components of CXY, for X and Y depending on the given intersection problem. The cone CXY is usually not reduced,...

Optimal Cones Intersection Technique

This paper presents an extension to the classical Cones Intersection Technique, which was, and is, exhaustively used to estimate the spin axis direction of spin stabilized spacecraft. The resulting Optimal Cones Intersection Technique is derived from a demonstrated co-planarity condition and does not present ambiguities or singularities. The proposed method allows an optimal estimation of any o...

K-Theory and Intersection Theory

2.1 Dimension and codimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Dimension relative to a base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Cartier divisors . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Intersection Theory Classes 20 and 21: Bivariant Intersection Theory

Intersection Theory

I provide more details to the intersection theoretic results in [1]. CONTENTS 1. Transversality and tubular neighborhoods 1 2. The Poincaré dual of a submanifold 4 3. Smooth cycles and their intersections 8 4. Applications 14 5. The Euler class of an oriented rank two real vector bundle 18 References 20 1. TRANSVERSALITY AND TUBULAR NEIGHBORHOODS We need to introduce a bit of microlocal termino...