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Kiyoshi Takeuchi

Publications and source records attributed to Kiyoshi Takeuchi.

33 records · Page 2Linked to original sources
arXiv2015

Hyperbolic localization and Lefschetz fixed point formulas for higher-dimensional fixed point sets

We study Lefschetz fixed point formulas for constructible sheaves with higher-dimensional fixed point sets. Under fairly weak assumptions, we prove that the local contributions from them are expressed by some constructible functions associated to hyperbolic localizations. This gives an affirmative answer to a conjecture of Goresky-MacPherson in particular for smooth fixed point components. In the course of the proof, the new Lagrangian cycles introduced in our previous paper will be effectively used. Moreover we show various examples for which local contributions can be explicitly determined by our method.

math.AG↗
arXiv2014

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.

math.AG↗
arXiv2013

Invertible polynomial mappings via Newton non-degeneracy

We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.

math.AG↗
arXiv2012

Monodromies at infinity of non-tame polynomials

We consider the monodromy at infinity and the monodromies around the bifurcation points of polynomial functions $f : \CC^n \longrightarrow \CC$ which are not tame and might have non-isolated singularities. Our description of their Jordan blocks in terms of the Newton polyhedra and the motivic Milnor fibers relies on two new issues: the non-atypical eigenvalues of the monodromies and the corresponding concentration results for their generalized eigenspaces.

math.AG↗
arXiv2012

Motivic Milnor fibers and Jordan normal forms of Milnor monodromies

By calculating the equivariant mixed Hodge numbers of motivic Milnor fibers introduced by Denef-Loeser, we obtain explicit formulas for the Jordan normal forms of Milnor monodromies. The numbers of the Jordan blocks will be described by the Newton polyhedron of the polynomial.

math.AG↗
arXiv2009

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.

math.AG↗
arXiv2009

Coefficients of the poles of local zeta functions and their applications to oscillating integrals

We introduce a new method which enables us to calculate the coefficients of the poles of local zeta functions very precisely and prove some explicit formulas. Some vanishing theorems for the candidate poles of local zeta functions will be also given. Moreover we apply our method to oscillating integrals and obtain an explicit formula for the coefficients of their asymptotic expansions.

math.CV↗
arXiv2008

A geometric degree formula for $A$-discriminants and Euler obstructions of toric varieties

We give explicit formulas for the dimensions and the degrees of $A$-discriminant varieties introduced by Gelfand-Kapranov-Zelevinsky. Our formulas can be applied also to the case where the $A$-discriminant varieties are higher-codimensional and their degrees are described by the geometry of the configurations $A$. Moreover combinatorial formulas for the Euler obstructions of general (not necessarily normal) toric varieties will be also given.

math.AG↗
arXiv2008

Monodromy at infinity of $A$-hypergeometric functions and toric compactifications

We study $A$-hypergeometric functions introduced by Gelfand-Kapranov-Zelevinsky and prove a formula for the eigenvalues of their monodromy automorphisms defined by the analytic continuaions along large loops contained in complex lines parallel to the coordinate axes. A method of toric compactifications will be used to prove our main theorem.

math.AG↗
arXiv2008

Milnor fibers over singular toric varieties and nearby cycle sheaves

We propose a new sheaf-theoretical method for the calculation of the monodromy zeta functions of Milnor fibrations. As an application, classical formulas of Kushnirenko and Varchenko etc. concerning polynomials on $\CC^n$ will be generalized to polynomial functions on any toric variety.

math.AG↗