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ON COMPLEX HOMOGENEOUS SINGULARITIES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 100 / Issue 3 / December 2019
- Published online by Cambridge University Press:
- 27 May 2019, pp. 395-409
- Print publication:
- December 2019
-
- Article
- Export citation
-
We study the singularity at the origin of
$\mathbb{C}^{n+1}$ of an arbitrary homogeneous polynomial in 
$n+1$ variables with complex coefficients, by investigating the monodromy characteristic polynomials 
$\unicode[STIX]{x1D6E5}_{l}(t)$ as well as the relation between the monodromy zeta function and the Hodge spectrum of the singularity. In the case 
$n=2$, we give a description of 
$\unicode[STIX]{x1D6E5}_{C}(t)=\unicode[STIX]{x1D6E5}_{1}(t)$ in terms of the multiplier ideal.
