Subextremal curves

Nollet, Scott

doi:10.1007/bf02677855

Cited by 24 publications

(34 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By liaison (see e.g. [14]) one has: [16]. The conclusion follows by the definition of extremal curves.…”

Section: Theorem 35 Let C Be a Curve Of Subextremal Type Of Degree mentioning

confidence: 84%

“…(v) If C is subextremal, then it is not minimal (see [16]). Conversely assume C is not subextremal; then C lies in a double plane 2H by (iv) and Z is not collinear by (iii).…”

Section: Theorem 35 Let C Be a Curve Of Subextremal Type Of Degree mentioning

confidence: 98%

“…Subextremal curves are classified in [16]. We will see that the subextremal curves of degree d and genus g form a smooth irreducible family F SE of dimension 2r + 6 + (d−2)(d+1) 2 , provided r 3, where r := d−3 2 + 1 − g is the maximum value of the Rao function (cf.…”

Section: Extremal and Subextremal Curvesmentioning

confidence: 99%

See 2 more Smart Citations

Families of space curves with large cohomology

2007

View full text Add to dashboard Cite

We investigate space curves with large cohomology. To this end we introduce curves of subextremal type. This class includes all subextremal curves. Based on geometric and numerical characterizations of curves of subextremal type, we show that, if the cohomology is "not too small," then they can be parameterized by the union of two generically smooth irreducible families; one of them corresponds to the subextremal curves. For curves of negative genus, the general curve of each of these families is also a smooth point of the support of an irreducible component of the Hilbert scheme. The two components have the same (large) dimension and meet in a subscheme of codimension one.

show abstract

“…By liaison (see e.g. [14]) one has: [16]. The conclusion follows by the definition of extremal curves.…”

Section: Theorem 35 Let C Be a Curve Of Subextremal Type Of Degree mentioning

confidence: 84%

“…(v) If C is subextremal, then it is not minimal (see [16]). Conversely assume C is not subextremal; then C lies in a double plane 2H by (iv) and Z is not collinear by (iii).…”

Section: Theorem 35 Let C Be a Curve Of Subextremal Type Of Degree mentioning

confidence: 98%

See 1 more Smart Citation

Families of space curves with large cohomology

2007

View full text Add to dashboard Cite

show abstract

“…We now give an example of how one can use Proposition 4.2 even when Q is not integral; for an application see [11]. Proposition 4.3.…”

Section: Furthermore If L Is a Line Which Meets Neither C Nor D Thementioning

confidence: 99%

A speciality theorem for Cohen-Macaulay space curves

Schlesinger

1999

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…In this direction S. Nollet in [19] showed that excluding the extremal curves the remaining ones are such that their Rao function ρ C (j) is in turn maximized by a function ρ SE (j); the curves which attain such maximal value are called "subextremal curves".…”

Section: Introductionmentioning

confidence: 99%

Characterizations of space curves containing a planar subcurve

Greco

Paxia

2010

Collect. Math.

View full text Add to dashboard Cite

We introduce and study the space curves of "h-extremal type", that are curves of degree d and arithmetic genus g whose Rao function agrees, in a suitable interval depending on d and h, with the one of the "h-extremal"curves introduced by Notari-Sabadini. Our study is motivated by the literature of the last years concerning curves with large cohomology and their relations with the Hilbert scheme.Our main result is a Structure Theorem which gives some geometrical characterizations of such curves. The most intriguing is that if d is sufficiently large with respect to h, a curve of h-extremal type contains a planar subcurve of degree d − h and lies on a non integral quadric. As a consequence we can determine all possible Rao functions (for fixed d, g, h). We add several examples which show, in particular, that our result is the best possible for h ≤ 5.

show abstract

Subextremal curves

Cited by 24 publications

References 2 publications

Families of space curves with large cohomology

Families of space curves with large cohomology

A speciality theorem for Cohen-Macaulay space curves

Characterizations of space curves containing a planar subcurve

Contact Info

Product

Resources

About