1. CMB Online first
||A Riemann-Hurwitz Theorem for the Algebraic Euler Characteristic|
We prove an analogue of the Riemann-Hurwitz theorem for computing
Euler characteristics of pullbacks of coherent sheaves through
finite maps of smooth projective varieties in arbitrary dimensions,
subject only to the condition that the irreducible components
of the branch and ramification locus have simple normal crossings.
Keywords:Riemann-Hurwitz, logarithmic-Chern class, Euler characteristic
2. CMB 2011 (vol 55 pp. 368)
||The Secondary Chern-Euler Class for a General Submanifold|
We define and study the secondary Chern-Euler class for a general submanifold of a Riemannian manifold. Using this class, we define and study the index for a vector field with non-isolated singularities on a submanifold. As an application, we give conceptual proofs of a result of Chern.
Keywords:secondary Chern-Euler class, normal sphere bundle, Euler characteristic, index, non-isolated singularities, blow-up