Abstract
For a very ample line bundle L on a projective scheme X, let φLℓ : X {right arrow, hooked} P H0 (X, Lℓ), ℓ ≥ 1, be the embedding defined by the complete linear series | Lℓ |. In this paper we study the problem how the Castelnuovo-Mumford regularity of φL (X) effects on the defining equations of φLℓ (X) and the syzygies among them. We show that if φL (X) ⊂ P H0 (X, L) is m-regular, then (X, Lℓ) satisfies property N2 ℓ - m + 1 for frac(m, 2) ≤ ℓ ≤ m - 2, and (X, Lℓ) satisfies property Nℓ for all ℓ ≥ m - 1.
Original language | English |
---|---|
Pages (from-to) | 108-121 |
Number of pages | 14 |
Journal | Journal of Algebra |
Volume | 322 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2009 Jul 1 |
Keywords
- Algebraic geometry
- Minimal free resolution
- Projective variety
ASJC Scopus subject areas
- Algebra and Number Theory