Koszul cohomology and the geometry of projective varieties

@article{Green1984KoszulCA,
  title={Koszul cohomology and the geometry of projective varieties},
  author={M. Green},
  journal={Journal of Differential Geometry},
  year={1984},
  volume={19},
  pages={125-171}
}
  • M. Green
  • Published 1984
  • Mathematics
  • Journal of Differential Geometry
FOURTH VERONESE EMBEDDINGS OF PROJECTIVE SPACES
We prove that fourth Veronese embeddings of projective spaces satisfies property N9. This settle the Ottaviani-Paoletti conjecture for fourth Veronese embeddings.
SUBADDITIVITY OF SYZYGIES OF IDEALS AND RELATED PROBLEMS
In this paper we survey what is known about the maximal degrees of minimal syzygies of graded ideals over polynomial rings. Subadditivity is one such property that is conjectured to hold for certainExpand
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Sharp bounds for higher linear syzygies and classifications of projective varieties
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Asymptotic syzygies of algebraic varieties
We study the asymptotic behavior of the syzygies of a smooth projective variety as the positivity of the embedding line bundle grows. The main result asserts that the syzygy modules are non-zero inExpand
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We study the Betti tables of reducible algebraic curves with a focus on connected line arrangements and provide a general formula for computing the quadratic strand of the Betti table for lineExpand
Local positivity, multiplier ideals, and syzygies of abelian varieties
We use the language of multiplier ideals in order to relate the syzygies of an abelian variety in a suitable embedding with the local positivity of the line bundle inducing that embedding. ThisExpand
green's canonical syzygy conjecture for generic curves of odd genus
  • C. Voisin
  • Mathematics
  • Compositio Mathematica
  • 2005
we prove in this paper the green conjecture for generic curves of odd genus. that is, we prove the vanishing $k_{k,1}(x,k_x)=0$ for x a generic curve of genus $2k+1$. this completes our previousExpand
A result on resolutions of Veronese embeddings
SuntoL’argomento di questo articolo sono le sizigie degli ideali delle varietà di Veronese. Per il teorema di Green sappiamo cheOPn(d) soddisfa la proprietàNp di Green-Lazarsfeld ∀d≥p, ∀n. Per ilExpand
Noether-Lefschetz locus for surfaces
We generalize M. Green's Explicit Noether-Lefschetz Theorem to the family of smooth complete intersection surfaces in the higher dimensional projective spaces. Moreover, we give a new proof of theExpand
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