# On the projective normality and normal presentation on higher dimensional varieties with nef canonical bundle

@article{Mukherjee2019OnTP, title={On the projective normality and normal presentation on higher dimensional varieties with nef canonical bundle}, author={Jayan Mukherjee and Debaditya Raychaudhury}, journal={Journal of Algebra}, year={2019} }

## 2 Citations

Effective global generation on varieties with numerically trivial canonical class

- Mathematics
- 2018

We prove a Fujita-type theorem for varieties with numerically trivial canonical bundle. We deduce our result via a combination of algebraic and analytic methods, including the Kobayashi--Hitchin…

## References

SHOWING 1-10 OF 45 REFERENCES

Syzygies of surfaces of general type

- Mathematics
- 2010

We prove new results on projective normality, normal presentation and higher syzygies for a surface of general type X embedded by adjoint line bundles Lr = K + r B, where B is a base point free,…

Embedding theorems on hyperelliptic varieties

- Mathematics
- 2014

In this paper, we investigate linear systems on hyperelliptic varieties. We prove analogues of well-known theorems on abelian varieties, like Lefschetz’s embedding theorem and higher k-jet embedding…

Projective normality and syzygies of algebraic surfaces

- Mathematics
- 2015

In this work we develop new techniques to compute Koszul cohomology groups for several classes of varieties. As applications we prove results on projective normality and syzygies for algebraic…

Syzygies of projective surfaces: an overview

- Mathematics
- 1999

This is a survey article concerning the syzygies of projective smooth varieties, with particular emphasis on the surface case. It describes some special cases of surfaces in which the so-called Mukai…

On Fujita’s freeness conjecture for 3-folds and 4-folds

- Mathematics
- 1995

We shall prove a conjecture of T. Fujita on the freeness of the adjoint linear systems in some cases: Let X be a smooth projective variety of dimension n and H an ample divisor. Assume that n = 3 or…

Normal generation of vector bundles over a curve

- Mathematics
- 1994

This characterization means normal generation allows us to calculate dimensions of the spaces of quadrics, cubics, and so forth which vanish on X, using Riemann-Roch. So we want optimal numerical…

Global generation of pluricanonical and adjoint linear series on smooth projective threefolds

- Mathematics
- 1993

The purpose of this paper is to show how the cohomological techniques developed by Kawamata, Reid, Shokurov, and others lead to some effective and practical results of Reider-type on freeness of…

Global generation of adjoint line bundles on projective 5-folds

- Mathematics
- 2014

Let X be a smooth projective variety of dimension 5 and L be an ample line bundle on X such that $$L^5>7^5$$L5>75 and $$L^d\cdot Z\ge 7^d$$Ld·Z≥7d for any subvariety Z of dimension $$1\le d\le…

The Chern Classes and Kodaira Dimension of a Minimal Variety

- Mathematics
- 1987

This paper deals with a sort of inequality for the first and second Chern classes of normal projective varieties with numerically effective canonical classes (Theorem 1.1); to some extent it is a…

Log canonical singularities are Du Bois

- Mathematics
- 2010

A recurring difficulty in the Minimal Model Program is that while log terminal singularities are quite well behaved (for instance, they are rational), log canonical singularities are much more…