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Non-isolated Hypersurface Singularities and L\^e Cycles
In this series of lectures, I will discuss results for complex hypersurfaces
with non-isolated singularities. In Lecture 1, I will review basic definitions
and results on complex hypersurfaces, and then present classical material on
the Milnor fiber and fibration. In Lecture 2, I will present basic results from
Morse theory, and use them to prove some results about complex hypersurfaces,
including a proof of L\^e's attaching result for Milnor fibers of non-isolated
hypersurface singularities. This will include defining the relative polar
curve. Lecture 3 will begin with a discussion of intersection cycles for proper
intersections inside a complex manifold, and then move on to definitions and
basic results on L\^e cycles and L\^e numbers of non-isolated hypersurface
singularities. Lecture 4 will explain the topological importance of L\^e cycles
and numbers, and then I will explain, informally, the relationship between the
L\^e cycles and the complex of sheaves of vanishing cycles.Comment: Notes from a series of lectures from the S\~ao Carlos singularities
meeting of 2014. Revision made to Exercise 3.1 (a