Alexander polynomial of plane algebraic curves and cyclic multiple planes

Libgober, Anatoly

doi:10.1215/s0012-7094-82-04941-9

Cited by 110 publications

(127 citation statements)

References 16 publications

Supporting

Mentioning

125

Contrasting

Order By: Relevance

“…Moreover, if C is irreducible, the order of a root of Δ C (t) cannot be a prime power [14]. Another general theorem on the Alexander polynomial is the following upper bound [8]: Let {L 1 , L 2 , . .…”

Section: Motivationmentioning

confidence: 99%

See 1 more Smart Citation

On the Alexander invariants of trigonal curves

Üçer

2021

Rev Mat Complut

View full text Add to dashboard Cite

We show that most of the genus-zero subgroups of the braid group B 3 (which are roughly the braid monodromy groups of the trigonal curves on the Hirzebruch surfaces) are irrelevant as far as the Alexander invariant is concerned: there is a very restricted class of "primitive" genus-zero subgroups such that these subgroups and their genus-zero intersections determine all the Alexander invariants. Then, we classify the primitive subgroups in a special subclass. This result implies the known classification of the dihedral covers of irreducible trigonal curves.

show abstract

Section: Motivationmentioning

confidence: 99%

“…. , (1 + λ) 8 } and m(m − λ) = 0. These two edges project into distinct orbits in P(k[λ]/λ 3 ), hence Ω contains only one of them.…”

Section: The Case P =mentioning

confidence: 99%

On the Alexander invariants of trigonal curves

Üçer

2021

Rev Mat Complut

View full text Add to dashboard Cite

show abstract

“…Zariski [14] found that the order cannot be the power of a prime for irreducible curves. Libgober [8] found that the order must divide the degree of the curve in general. He also found that the Alexander polynomial of a curve divides the product of the local Alexander polynomials at the singularities of the curve; that is, those of the associated links of the singularities.…”

Section: Introductionmentioning

confidence: 99%

On the Alexander Invariants of Trigonal Curves

Üçer

2020

Preprint

View full text Add to dashboard Cite

We show that most of the genus-zero subgroups of the braid group B 3 (which are roughly the braid monodromy groups of the trigonal curves on the Hirzebruch surfaces) are irrelevant as far as the Alexander module is concerned. There is a very restricted set of subgroups, which we call "primitive", such that these subgroups and their intersections determine all the Alexander modules. Then, we classify the primitive subgroups of genus zero which belong to a particular kind and compute their Alexander modules. This result implies, in particular, the known classification of the dihedral covers of the trigonal curves.

show abstract

“…It has integral coefficients. For the definition of the Alexander polynomial, we refer to [Li2]. We recall several basic properties of ~c ( t).…”

Section: Alexander Polynomialmentioning

confidence: 99%

“…(1) ~c(t) divides the Alexander polynomial at infinity (tnl)n-2 (t-1) M. Oka and also the product of the local Alexander polynomials at singular points of C ([Li2] and [Lill).…”

Section: Alexander Polynomialmentioning

confidence: 99%

Geometry of cuspidal sextics and their dual curves

Oka¹

Singularities – Sapporo 1998

View full text Add to dashboard Cite

show abstract

Alexander polynomial of plane algebraic curves and cyclic multiple planes

Cited by 110 publications

References 16 publications

On the Alexander invariants of trigonal curves

On the Alexander invariants of trigonal curves

On the Alexander Invariants of Trigonal Curves

Geometry of cuspidal sextics and their dual curves

Contact Info

Product

Resources

About