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The bifurcation set of a rational function via Newton polytopes
Tat Thang Nguyen, Takahiro Saito, Kiyoshi Takeuchi
The bifurcation sets of polynomial functions have been studied by many mathematicians from various points of view. In particular, Némethi and Zaharia described them in terms of New…
Uniform stable radius and Milnor number for non-degenerate isolated complete intersection singularities
Tat Thang Nguyen
We prove that for two germs of analytic mappings with the same Newton polyhedra which are (Khovanskii) non-degenerate and…
Meromorphic nearby cycle functors and monodromies of meromorphic functions (with Appendix by T. Saito)
Tat Thang Nguyen, Kiyoshi Takeuchi
We introduce meromorphic nearby cycle functors and study their functorial properties. Moreover we apply them to monodromies of meromorphic functions in various situations. Combinat…
Geometry of nondegenerate polynomials: Motivic nearby cycles and Cohomology of contact loci
Quy Thuong Lê, Tat Thang Nguyen
We study polynomials with complex coefficients which are nondegenerate in two senses, one of Kouchnirenko and the other with respect to its Newton polyhedron, through data on conta…
Bifurcation sets and global monodromies of Newton non-degenerate polynomials on algebraic sets
Tat Thang Nguyen, Phu Phat Pham, Tien-Son Pham
Let be a non-singular algebraic set and be a polynomial function. It is well-known that the restriction $f|_S \colon…