Monodromies at infinity of non-tame polynomials

On the sizes of the Jordan blocks of monodromies at infinity

We obtain general upper bounds of the sizes and the numbers of Jordan blocks for the eigenvalues $λ\not= 1$ in the monodromies at infinity of polynomial maps.

Monodromies at infinity of confluent A-hypergeometric functions

We study the monodromies at infinity of confluent A-hypergeometric functions introduced by Adolphson. In particular, we extend the result of the third author for non-confluent A-hypergeometric functions to the confluent case. The integral representation by rapid decay homology cycles will play a central role in the proof.

关于完整 D-模的 Fourier 变换在无穷远处的单值性

On the monodromies at infinity of Fourier transforms of holonomic D-modules

本文借助非正则 Riemann–Hilbert 对应和单值性 zeta 函数，研究完整 D-模 Fourier 变换解的无穷远单值性，给出特征值公式，并在一维情形建立互反律。

Bifurcation sets and global monodromies of Newton non-degenerate polynomials on algebraic sets

Let $S\subset \mathbb{C}^n$ be a non-singular algebraic set and $f \colon \mathbb{C}^n \to \mathbb{C}$ be a polynomial function. It is well-known that the restriction $f|_S \colon S \to \mathbb{C}$ of $f$ on $S$ is a locally trivial fibration outside a finite set $B(f|_S) \subset \mathbb{C}.$ In this paper, we give an explicit description of a finite set $T_\infty(f|_S) \subset \mathbb{C}$ such that $B(f|_S) \subset K_0(f|_S) \cup T_\infty(f|_S),$ where $K_0(f|_S)$ denotes the set of critical values of the $f|_S.$ Furthermore, $T_\infty(f|_S)$ is contained in the set of critical values of cert…

Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem

Let f be a definable function, enough differentiable. Under the condition of having strongly isolated singularities at infinity at a regular value c we give a sufficient condition expressed in terms of the total absolute curvature function to ensure the local triviality of the function f over a neighbourhood of c and doing so providing the tame version of Parusinski's Theorem on complex polynomials with isolated singularities at infinity.

Weight filtration of the limit mixed Hodge structure at infinity for tame polynomials

We give three new proofs of a theorem of C. Sabbah asserting that the weight filtration of the limit mixed Hodge structure at infinity of cohomologically tame polynomials coincides with the monodromy filtration up to a certain shift depending on the unipotent or non-unipotent monodromy part.