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The incidence class and the hierarchy of orbits

100%

Fehér L., Patakfalvi Z.

Open Mathematics

2009

tom 7

nr 3

429-441

R. Rimányi defined the incidence class of two singularities η and ζ as [η]|ζ, the restriction of the Thom polynomial of η to ζ. He conjectured that (under mild conditions) [η]|ζ ≠ 0 ⇔ ζ ⊂ $$ \bar \eta $$. Generalizing this notion we define the incidence class of two orbits η and ζ of a representation. We give a sufficient condition (positivity) for ζ to have the property that [η]|ζ ≠ 0 ⇔ ζ ⊂ $$ \bar \eta $$ for any other orbit η. We show that for many interesting cases, e.g. the quiver representations of Dynkin type positivity holds for all orbits. In other words in these cases the incidence classes completely determine the hierarchy of the orbits. We also study the case of singularities where positivity doesn’t hold for all orbits.

Milnor fibration at infinity for mixed polynomials

42%

Chen Y.

Open Mathematics

2014

tom 12

nr 1

28-38

We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial f: ℝ2n → ℝ2. By using strongly non-degenerate condition, we prove a counterpart of Némethi and Zaharia’s fibration theorem. In particular, we obtain a global version of Oka’s fibration theorem for strongly non-degenerate and convenient mixed polynomials.

Ograniczanie wyników

2 Open Mathematics

1 Chen Y.

1 Fehér L.

1 Patakfalvi Z.

1 2014

1 2009

Wyniki wyszukiwania

The incidence class and the hierarchy of orbits

Milnor fibration at infinity for mixed polynomials