On the existence of algebraic curves in projectiven-space

Pasarescu, Ovidiu

doi:10.1007/bf01207480

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1989

1991

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, since the degree d of the general Ct must be the degree of the given cycle, and the genus is given, a complete solution would tells us in particular for which triples (n, d, g) there are smooth curves of degree d and genus g in P", an open question for n ~> 6 (cf. [6] or [18]). Perhaps the problem will have, in general, a negative answer (cf.…”

Section: Introductionmentioning

confidence: 99%

On the geometric realization of Albanese's inequality

Nobile

1991

Geom Dedicata

View full text Add to dashboard Cite

If an algebraic curve C (irreducible and reduced) moving in a family in projective nspace specializes into a curve Co, having associated cycle Z = mlB1 + ... + m,B,, then the geometric genera g, gl,..., gr of C, BI,..., B r respectively and the coefficients m~,..., m, must satisfy a certain inequality (found by Albanese). The realization (or existence) problem asks whether an inequality of this type actually arises from an algebraic family of curves. In this paper some results are obtained concerning the strong version of the problem, where one specifies the cycle Z; with these an affirmative solution of the weak version (where the components B i are not specified) is obtained.

show abstract

Section: Introductionmentioning

confidence: 99%