Bifurcation values of mixed polynomials

Ying Chen (1) , Mihai Tibar (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We study the bifurcation locus $B(f)$ of real polynomials $f: \bR^{2n} \to \bR^2$. We find a semialgebraic approximation of $B(f)$ by using the $\rho$-regularity condition and we compare it to the Sard type theorem by Kurdyka, Orro and Simon. We introduce the Newton boundary at infinity for mixed polynomials and we extend structure results by Kushnirenko and by Némethi and Zaharia, under the Newton non-degeneracy assumption.

Domaines: Variables complexes [math.CV]; Géométrie algébrique [math.AG]; Topologie algébrique [math.AT]

Ying Chen, Mihai Tibar. Bifurcation values of mixed polynomials. Math. Research Letters, 2012, 19 (no.1), pp.59-79. ⟨hal-00568154⟩