The monodromy of reducible plane curves

Sumners, D. W.; Woods, J. M.

doi:10.1007/bf01390342

Cited by 20 publications

(27 citation statements)

References 15 publications

(21 reference statements)

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“…Here Y n−1 is one of two standard model spaces: complement in a torus T n either to a torus knot or to the union of the axis of the torus and the torus knot (cf. [26]). The union is taken by identifying the boundary of a tube about L n−1 with ∂T n .…”

Section: Characteristic Varieties Of Algebraic Linksmentioning

confidence: 99%

Hodge decomposition of Alexander invariants

Libgober¹

2002

manuscripta mathematica

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Section: Characteristic Varieties Of Algebraic Linksmentioning

confidence: 99%

Hodge decomposition of Alexander invariants

Libgober¹

2002

manuscripta mathematica

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“…For 3-dimensional Seifert-fibered knots /links the result, Eq. (5.27), had been obtained by Le Trang [150] and, independently, by Sumners and Woods [151]. The result, Eq.…”

Section: Connections Between Zeta Function and Alexander Polynomialmentioning

confidence: 74%

New String Amplitudes From Old Fermat (Hyper)surfaces

Kholodenko

2004

Int. J. Mod. Phys. A

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The history of the discovery of bosonic string theory is well documented. This theory evolved as an attempt to find a multidimensional analogue of Euler's beta function to describe the multiparticle Veneziano amplitudes. Such an analogue had in fact been known in mathematics at least in 1922. Its mathematical meaning was studied subsequently from different angles by mathematicians such as Selberg, Weil and Deligne among others. The mathematical interpretation of this multidimensional beta function that was developed subsequently is markedly different from that described in physics literature. This work aims to bridge the gap between the mathematical and physical treatments. Using some results of recent publications (e.g. J.Geom.Phys.38 (2001) 81 ; ibid 43 (2002) 45) new topological, algebro-geometric, number-theoretic and combinatorial treatment of the multiparticle Veneziano amplitudes is developed. As a result, an entirely new physical meaning of these amplitudes is emerging: they are periods of differential forms associated with homology cycles on Fermat (hyper)surfaces. Such (hyper)surfaces are considered as complex projective varieties of Hodge type. Although the computational formalism developed in this work resembles that used in mirror symmetry calculations, many additional results from mathematics are used along with their suitable physical interpretation. For instance, the Hodge spectrum of the Fermat (hyper)surfaces is in one-to-one correspondence with the possible spectrum of particle masses. The formalism also allows us to obtain correlation functions of both conformal field theory and particle physics using the same type of the Picard-Fuchs equations whose solutions are being interpreted in terms of periods.MSC: 81T30,81T40,81T99,81U99

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“…Remark. 21. The assumptions that X is a complex curve and non-singular are essential in Theorem 1 as seen from Remarks 19 and 20.…”

Section: Eras---rein+elmentioning

confidence: 95%

“…We remark that after the pioneering work of Milnor [14] on the links of singularities (see also A'Campo [1], L6 [12], Sumners and Woods [21] and Neumann [16]), topological properties of complex plane curves in not necessarily small or round balls were studied by Laufer [11] and more recently by Lee Rudolph. See [18] for a good introduction into the subject and additional references.…”

Section: Introductionmentioning

confidence: 99%

Complex plane curves in the ball

Fiedler

1989

Invent Math

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The monodromy of reducible plane curves

Cited by 20 publications

References 15 publications

Hodge decomposition of Alexander invariants

Hodge decomposition of Alexander invariants

New String Amplitudes From Old Fermat (Hyper)surfaces

Complex plane curves in the ball

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