# Linear syzygies, flag complexes, and regularity

@article{Constantinescu2015LinearSF, title={Linear syzygies, flag complexes, and regularity}, author={Alexandru Constantinescu and Thomas Kahle and Matteo Varbaro}, journal={Collectanea Mathematica}, year={2015}, volume={67}, pages={357-362} }

We show that for every $$r\in \mathbb {Z}_{>0}$$r∈Z>0 there exist monomial ideals generated in degree two, with linear syzygies, and regularity of the quotient equal to $$r$$r. For Gorenstein ideals we prove that the regularity of their quotients can not exceed four, thus showing that for $$d > 4$$d>4 every triangulation of a $$d$$d-manifold has a hollow square or simplex. We also show that for most monomial ideals generated in degree two and with linear syzygies the regularity is $$O(\log…

## 4 Citations

Linearity of free resolutions of monomial ideals

- MathematicsResearch in the Mathematical Sciences
- 2022

We study monomial ideals with linear presentation or partially linear resolution. We give combinatorial characterizations of linear presentation for square-free ideals of degree 3, and for primary…

Linear syzygies, hyperbolic Coxeter groups and regularity

- MathematicsCompositio Mathematica
- 2019

We show that the virtual cohomological dimension of a Coxeter group is essentially the regularity of the Stanley–Reisner ring of its nerve. Using this connection between geometric group theory and…

Subadditivity of Syzygies of Ideals and Related Problems

- MathematicsCommutative Algebra
- 2021

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…

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