Planning
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Friday, October 1, 2021 |
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08:00
09:00
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11:00
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17:00
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›9:50 (50min)
H. HAMM (via ZOOM ) : Holomorphic mappings and Milnor fibrations Holomorphic functions, i.e. holomorphic mappings $f:X\to\mathbb{C}$, $(X,0)$ being a complex analytic subgerm of $\mathbb{C}^N,0)$, lead to a Milnor fibration without the hypothesis of having an isolated singularity - this is due to the existence of stratifications of $X$ with Thom's $a_f$ condition. The situation changes radically, of course, in the case of mappings to $f:X\to \mathbb{C}^k, k>1$. A typical example is a blowing-up: $f:\mathbb{C}^2\to\mathbb{C}^2, (z_1,z_2) mapsto (z_1,z_1z_2)$. For instance, the image of $f|B_\epsilon\cap f^{-1}(D_\alpha)$, $0<\alpha\ll\epsilon$, depends on the radius $\epsilon$ and is merely semianalytic. It turns out that these two phenomena are not independent. Here it is helpful to have some evaluative criterion for complex constructibility, applied to a direct image sheaf in our case. Altogether, heavy restrictions on $f$ are necessary in order to have a similar situation as in the case $k=1$.
›11:00 (50min)
LE DUNG TRANG (à la Frumam) : Condition de Thom pour une stratification : Dans le cas d'un morphisme entre espaces analytiques complexes, on considère le cas de morphismes stratifiés. Pour morphismes stratifiés d'espaces analytiques complexes, Thom a introduit une condition appelée par Thom de morphismes sans éclatement et qu'on appelle maintenant la condition de Thom. Nous donnons la définition de la condition de Thom et nous montrons l'importance de cette condition dans l'étude de la Topologie locale d'un morphisme stratifié.
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