Bifurcation values of polynomial functions and perverse sheaves

We characterize bifurcation values of polynomial functions by using the theory of perverse sheaves and their vanishing cycles. In particular, by introducing a method to compute the jumps of the Euler characteristics with compact support of their fibers, we confirm the conjecture of N\'emethi-Zaharia in many cases.Comment: 19 pages, to appear in Annales de l'Institut Fourie

Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves

By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained.Comment: 31 pages; revise