arXiv subjects

Yutaka Matsui

Publications and source records attributed to Yutaka Matsui.

8 recordsLinked 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↗

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↗

arXiv2012

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.

math.AG↗

arXiv2012

Monodromy at infinity of polynomial maps and Newton polyhedra (with Appendix by C. Sabbah)

By introducing motivic Milnor fibers at infinity of polynomial maps, we propose some methods for the study of nilpotent parts of monodromies at infinity. The numbers of Jordan blocks in the monodromy at infinity will be described by the Newton polyhedron at infinity 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↗

arXiv2008

Microlocal study of Lefschetz fixed point formulas for higher-dimensional fixed point sets

We introduce new Lagrangian cycles which encode local contributions of Lefschetz numbers of constructible sheaves into geometric objects. We study their functorial properties and apply them to Lefschetz fixed point formulas with higher-dimensional fixed point sets.

math.AG↗

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

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↗