Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T01:13:18.671Z Has data issue: false hasContentIssue false

ALEXANDER POLYNOMIALS OF COMPLEX PROJECTIVE PLANE CURVES

Published online by Cambridge University Press:  07 March 2018

QUY THUONG LÊ*
Affiliation:
Department of Mathematics, Vietnam National University, Hanoi, 334 Nguyen Trai Street, Thanh Xuan District, Hanoi, Vietnam email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We compute the Alexander polynomial of a nonreduced nonirreducible complex projective plane curve with mutually coprime orders of vanishing along its irreducible components in terms of certain multiplier ideals.

Type
Research Article
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Bartolo, E. A., ‘Sur les couples de Zariski’, J. Algebraic Geom. 3 (1994), 223247.Google Scholar
Budur, N., ‘Unitary local systems, multiplier ideals, and polynomial periodicity of Hodge numbers’, Adv. Math. 221(1) (2009), 217250.CrossRefGoogle Scholar
Budur, N., ‘Hodge spectrum of hyperplane arrangements’, Preprint, 2008, arXiv:0809.3443; incorporated in N. Budur and M. Saito, ‘Jumping coefficients and spectrum of a hyperplane arrangement’, Math. Ann. 347(3) (2010), 545–579.Google Scholar
Budur, N., Multiplier Ideals, Milnor Fibers, and Other Singularity Invariants, Lecture Notes, (Luminy, 2011). https://perswww.kuleuven.be/∼u0089821/LNLuminy.pdf.Google Scholar
Esnault, H., ‘Fibre de Milnor d’un cône sur une courbe plane singulilarité’, Invent. Math. 68 (1982), 477496.Google Scholar
van Kampen, E. R., ‘On the fundamental group of an algebraic curve’, Amer. J Math. 55 (1933), 255267.CrossRefGoogle Scholar
Lazarsfeld, R., Positivity in Algebraic Geometry II - Positivity for Vector Bundles, and Multiplier Ideals (Springer, Berlin, 2004).CrossRefGoogle Scholar
Libgober, A., ‘Alexander polynomial of plane algebraic curves and cyclic multiple planes’, Duke Math. J. 49 (1982), 833851.CrossRefGoogle Scholar
Libgober, A., ‘Alexander invariants of plane albebraic curves’, Proc. Sympos. Pure Math. 40 (1983), 135143.Google Scholar
Loeser, F. and Vaquié, M., ‘Le polynôme d’Alexander d’une courbe plane projective’, Topology 29 (1990), 163173.Google Scholar
Milnor, J., ‘Singular points of complex hypersurfaces’, in: Ann. Math. Studies, Vol. 61 (Princeton University Press, Princeton, 1968).Google Scholar
Randell, R., ‘Milnor fibers and Alexander polynomials of plane curves’, Proc. Sympos. Pure Math. 40 (1983), 415419.Google Scholar