Constructing schemes with prescribed cohomology in arbitrary codimension

Migliore, Juan; Nagel, Uwe; Peterson, Chris

doi:10.1016/s0022-4049(99)00136-x

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2000

2012

Publication Types

Select...

Article5

Relationship

Self Cite1

Independent4

Authors

Journals

Cited by 7 publications

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[21]). However, fixing the degree d and the (arithmetic) genus g puts restrictions on the possible Hartshorne-Rao modules.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-degenerate curves with maximal Hartshorne-Rao module

Nagel

2003

Mathematische Zeitschrift

Self Cite

View full text Add to dashboard Cite

Abstract. Extending results for space curves we establish bounds for the cohomology of a non-degenerate curve in projective n-space. As a consequence, for any given n we determine all possible pairs (d, g) where d is the degree and g is the (arithmetic) genus of the curve. Furthermore, we show that curves attaining our bounds always exist and describe properties of these extremal curves. In particular, we determine the HartshorneRao module, the generic initial ideal and the graded Betti numbers of an extremal curve.

show abstract

“…[21]). However, fixing the degree d and the (arithmetic) genus g puts restrictions on the possible Hartshorne-Rao modules.…”

Section: Introductionmentioning

confidence: 99%

“…Every graded module of finite length is (up to degree shift) the Hartshorne-Rao module of a curve (cf. [21]). However, fixing the degree d and the (arithmetic) genus g puts restrictions on the possible Hartshorne-Rao modules.…”

Section: Introductionmentioning

confidence: 99%