TOPOLOGICAL ZETA FUNCTIONS OF COMPLEX PLANE CURVE SINGULARITIES

被引：0

作者：

Le, Quy Thuong ^{[1
]}

Nguyen, Khanh Hung ^{[2
]}

机构：

[1] Vietnam Natl Univ, VNU Univ Sci, 334 Nguyen Trai St, Hanoi, Vietnam

[2] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet Rd, Hanoi, Vietnam

来源：

OSAKA JOURNAL OF MATHEMATICS | 2023年 / 60卷 / 02期

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study topological zeta functions of complex plane curve singularities using toric modifications and further developments. As applications of the research method, we prove that the topological zeta function is a topological invariant for complex plane curve singularities, we give a short and new proof of the monodromy conjecture for plane curves.

引用

页码：305 / 321

页数：17

共 50 条

[1] MOTIVIC ZETA FUNCTIONS FOR CURVE SINGULARITIES
Moyano-Fernandez, J. J.
Zuniga-Galindo, W. A.
[J]. NAGOYA MATHEMATICAL JOURNAL, 2010, 198 : 47 - 75
[2] ZETA-POLYNOMIALS, SUPERPOLYNOMIALS, DAHA AND PLANE CURVE SINGULARITIES
Cherednik, Ivan
[J]. arXiv, 2023,
[3] Poles of the complex zeta function of a plane curve
Blanco, Guillem
[J]. ADVANCES IN MATHEMATICS, 2019, 350 : 396 - 439
[4] Poincaré series and zeta-function for irreducible plane curve singularities
Stevens J.
[J]. Journal of Mathematical Sciences, 2007, 144 (1) : 3848 - 3853
[5] TOPOLOGICAL CLASSIFICATION OF IRREDUCIBLE PLANE CURVE SINGULARITIES IN TERMS OF WEIERSTRASS POLYNOMIALS
KANG, CY
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (05) : 1363 - 1371
[6] The Alexander polynomial of plane curve singularities and rings of functions on curves
Gusein-Zade, SM
Delgado, F
Campillo, A
[J]. RUSSIAN MATHEMATICAL SURVEYS, 1999, 54 (03) : 634 - 635
[7] A note on complex plane curve singularities up to diffeomorphism and their rigidity
Fernandez-Hernandez, A.
Conejero, R. Gimenez
[J]. RESEARCH IN THE MATHEMATICAL SCIENCES, 2024, 11 (02)
[8] Topological invariants of plane curve singularities: Polar quotients and Lojasiewicz gradient exponents
Hong-Duc Nguyen
Tien-Son Pham
Phi-Dung Hoang
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2019, 30 (14)
[9] Plane curve singularities and carousels
Tráng, LD
[J]. ANNALES DE L INSTITUT FOURIER, 2003, 53 (04) : 1117 - +
[10] On the equivalence of plane curve singularities
Waldi, R
[J]. COMMUNICATIONS IN ALGEBRA, 2000, 28 (09) : 4389 - 4401

← 1 2 3 4 5 →