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In this paper we characterize the Blowing-up maps of ordinary singularities for which there exists a natural Gysin morphism, i.e. a bivariant class $theta in Hom_{D(Y)}(Rpi_*mathbb Q_X, mathbb Q_Y)$, compatible with pullback and with restriction to the complement of the singularity.
We propose a general definition of mathematical instanton bundle with given charge on any Fano threefold extending the classical definitions on $mathbb P^3$ and on Fano threefold with cyclic Picard group. Then we deal with the case of the blow up of
We prove a monomialization theorem for mappings in general classes of infinitely differentiable functions that are called quasianalytic. Examples include Denjoy-Carleman classes (of interest in real analysis), the class of infinitely differentiable f
We introduce a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing over a finite field. Extending a result of Benoist, we prove that for a morphism $phi colon X to mathbb{P}^n$ such that $X$ i
We study finite time blow-up and global existence of solutions to the Cauchy problem for the porous medium equation with a variable density $rho(x)$ and a power-like reaction term. We show that for small enough initial data, if $rho(x)sim frac{1}{lef
We consider the nonlinear heat equation with a nonlinear gradient term: $partial_t u =Delta u+mu| abla u|^q+|u|^{p-1}u,; mu>0,; q=2p/(p+1),; p>3,; tin (0,T),; xin R^N.$ We construct a solution which blows up in finite time $T>0.$ We also give a sharp