## Journal of the Mathematical Society of Japan

### On the Seifert form at infinity associated with polynomial maps

András NÉMETHI

#### Abstract

If apolynomial map $f$ : $C^{n}\rightarrow C$ has anice behaviour at infinity (e.g. it is a "good polynomial"), then the Milnor fibration at infinity exists; in particular, one can define the Seifert form at infinity $\Gamma(f)$ associated with $f$. In this paper we prove a Sebastiani-Thom type formula. Namely, if $f$ : $C^{n}\rightarrow C$ and $g:c^{m}\rightarrow C$ are "good" polynomials, and we define $h=f$$\oplus$$g$ : $C^{n+m}\rightarrow C$ by $h(x,y)=f(x)+g(y)$, then $\Gamma(h)=(-\mathrm{I})^{mn}\Gamma(f)$$\otimes\Gamma(g)$. This is the global analogue of the local result, proved independently by K. Sakamoto and P. Deligne for isolated hypersurface singularities.

#### Article information

Source
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 63-70.

Dates
First available in Project Euclid: 10 June 2008

https://projecteuclid.org/euclid.jmsj/1213108351

Digital Object Identifier
doi:10.2969/jmsj/05110063

Mathematical Reviews number (MathSciNet)
MR1660996

Zentralblatt MATH identifier
0933.32042

#### Citation

NÉMETHI, András. On the Seifert form at infinity associated with polynomial maps. J. Math. Soc. Japan 51 (1999), no. 1, 63--70. doi:10.2969/jmsj/05110063. https://projecteuclid.org/euclid.jmsj/1213108351