Generic invertible sheaves of 2-torsion and generic invertible thetacharacteristics on nodal plane curves

Weierstrass gap sequence at total inflection points of nodal plane curves

Tsukuba Journal of Mathematics ◽

10.21099/tkbjm/1496162458 ◽

1994 ◽

Vol 18 (1) ◽

pp. 119-129 ◽

Cited By ~ 3

Author(s):

Marc Coppens ◽

Takao Kato

Keyword(s):

Plane Curves ◽

Nodal Plane ◽

Inflection Points ◽

Gap Sequence ◽

Weierstrass Gap Sequence

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Nodal curves with a contact-conic and Zariski pairs

Advances in Geometry ◽

10.1515/advgeom-2018-0032 ◽

2019 ◽

Vol 19 (4) ◽

pp. 555-572 ◽

Cited By ~ 1

Author(s):

Shinzo Bannai ◽

Taketo Shirane

Keyword(s):

Plane Curves ◽

Nodal Plane ◽

Nodal Curves ◽

Splitting Type

Abstract To study the splitting of nodal plane curves with respect to contact conics, we define the splitting type of such curves and show that it can be used as an invariant to distinguish the embedded topology of plane curves. We also give a criterion to determine the splitting type in terms of the configuration of the nodes and tangent points. As an application, we construct sextics and contact conics with prescribed splitting types, which give rise to new Zariski-triples.

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Plane Curves With Nodes

Canadian Journal of Mathematics ◽

10.4153/cjm-1989-010-x ◽

1989 ◽

Vol 41 (2) ◽

pp. 193-212 ◽

Cited By ~ 2

Author(s):

Robert Treger

Keyword(s):

General Position ◽

Algebraic Curve ◽

Plane Curve ◽

Exceptional Case ◽

Plane Curves ◽

Nodal Plane ◽

Nodal Curve

A smooth algebraic curve is birationally equivalent to a nodal plane curve. One of the main problems in the theory of plane curves is to describe the situation of nodes of an irreducible nodal plane curve (see [16, Art. 45], [10], [7, Book IV, Chapter I, §5], [12, p. 584], and [3]).Let n denote the degree of a nodal curve and d the number of nodes. The case (AZ, d) — (6,9) has been analyzed by Halphen [10]. It follows from Lemma 3.5 and Proposition 3.6 that this is an exceptional case. The case d ≦n(n + 3)/6, d ≦(n — 1)(n — 2)/2, and (n, d) ≠ (6,9) was investigated by Arbarello and Cornalba [3]. We present a simpler proof (Corollary 3.8).We consider the main case which is particularly important due to its applications to the moduli variety of curves, compare [19, Chapter VIII, Section 4]. Let Vn,d be the variety of irreducible curves of degree n with d nodes and no other singularities such that each curve of Vn,d can be degenerated into n lines in general position (see [17]).

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