#### 535 Citations

FOURTH VERONESE EMBEDDINGS OF PROJECTIVE SPACES

- 2014

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

- 2020

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 certain… Expand

The canonical syzygy conjecture for ribbons

- Mathematics
- 2018

Green’s canonical syzygy conjecture asserts a simple relationship between the Clifford index of a smooth projective curve and the shape of the minimal free resolution of its homogeneous ideal in the… Expand

Sharp bounds for higher linear syzygies and classifications of projective varieties

- Mathematics
- 2015

In the present paper, we consider upper bounds of higher linear syzygies i.e. graded Betti numbers in the first linear strand of the minimal free resolutions of projective varieties in arbitrary… Expand

Asymptotic syzygies of algebraic varieties

- Mathematics
- 2012

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 in… Expand

Betti tables of reducible algebraic curves

- Mathematics
- 2012

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 line… Expand

Local positivity, multiplier ideals, and syzygies of abelian varieties

- Mathematics
- 2010

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. This… Expand

green's canonical syzygy conjecture for generic curves of odd genus

- 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 previous… Expand

A result on resolutions of Veronese embeddings

- Mathematics
- 2004

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 il… Expand

Noether-Lefschetz locus for surfaces

- Mathematics
- 1991

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 the… Expand