k-th Milnor numbers and k-th Tjurina numbers of weighted homogeneous singularities

Naveed Hussain; Zhiwen Liu; Stephen S.T. Yau; Huaiqing Zuo

doi:10.1007/s10711-023-00768-0

k-th Milnor numbers and k-th Tjurina numbers of weighted homogeneous singularities

Naveed Hussain
, Zhiwen Liu
, Stephen S.T. Yau^*
, Huaiqing Zuo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let (V, 0) ⊂ (Cⁿ, 0) be a weighted homogeneous isolated hypersurface singularity. In this paper, we give explicit formulas of its k-th Milnor numbers and the k-th Tjurina numbers in terms of its weight type. Moreover, we propose a sharp lower bound conjecture for the k-th Tjurina numbers and verify this conjecture for binomial singularities. We also give a new characterization for the simple hypersurface singularities.

Original language	English
Article number	34
Journal	Geometriae Dedicata
Volume	217
Issue number	2
DOIs	https://doi.org/10.1007/s10711-023-00768-0
State	Published - Apr 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature B.V.

Keywords

Derivation Lie algebra
Isolated singularity
Moduli algebra
Weighted homogeneous

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-023-00768-0

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title = "k-th Milnor numbers and k-th Tjurina numbers of weighted homogeneous singularities",

abstract = "Let (V, 0) ⊂ (Cn, 0) be a weighted homogeneous isolated hypersurface singularity. In this paper, we give explicit formulas of its k-th Milnor numbers and the k-th Tjurina numbers in terms of its weight type. Moreover, we propose a sharp lower bound conjecture for the k-th Tjurina numbers and verify this conjecture for binomial singularities. We also give a new characterization for the simple hypersurface singularities.",

keywords = "Derivation Lie algebra, Isolated singularity, Moduli algebra, Weighted homogeneous",

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AU - Zuo, Huaiqing

PY - 2023/4

Y1 - 2023/4

N2 - Let (V, 0) ⊂ (Cn, 0) be a weighted homogeneous isolated hypersurface singularity. In this paper, we give explicit formulas of its k-th Milnor numbers and the k-th Tjurina numbers in terms of its weight type. Moreover, we propose a sharp lower bound conjecture for the k-th Tjurina numbers and verify this conjecture for binomial singularities. We also give a new characterization for the simple hypersurface singularities.

AB - Let (V, 0) ⊂ (Cn, 0) be a weighted homogeneous isolated hypersurface singularity. In this paper, we give explicit formulas of its k-th Milnor numbers and the k-th Tjurina numbers in terms of its weight type. Moreover, we propose a sharp lower bound conjecture for the k-th Tjurina numbers and verify this conjecture for binomial singularities. We also give a new characterization for the simple hypersurface singularities.

KW - Derivation Lie algebra

KW - Isolated singularity

KW - Moduli algebra

KW - Weighted homogeneous

UR - https://www.scopus.com/pages/publications/85146561826

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DO - 10.1007/s10711-023-00768-0

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ER -

k-th Milnor numbers and k-th Tjurina numbers of weighted homogeneous singularities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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