#### Jörg Schürmann

University of Münster

### Resumen:

Let $X$ and $Y$ be closed complex subvarieties in an ambient
complex manifold $M$. We will explain the intersection formula
$$c(X) \cdot c(Y)= c(TM)\cap c(X\cap Y)$$
for suitable notions of Chern classes and transversality for singular spaces.
If $X$ and $Y$ intersect transversal in a Whitney stratified sense, this is
true for the MacPherson Chern classes (of adopted constructible functions).
If $X$ and $Y$ are "splayed" in the sense of Aluffi-Faber, then this formula
holds for the Fulton-(Johnson-) Chern classes, and is conjectured for the
MacPherson Chern classes.

We explain, that the version for the MacPherson Chern classes is true under a
micro-local "non-characteristic" condition for the diagonal embedding of $M$
with respect to $X\times Y$. This notion of non-characteristic is weaker than
the Whitney stratified transversality as well as the splayedness assumption.

### Presentación:

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