## Abstract

Geometric vertex decomposition and liaison are two frameworks that have been used to produce similar results about similar families of algebraic varieties. In this paper, we establish an explicit connection between these approaches. In particular, we show that each geometrically vertex decomposable ideal is linked by a sequence of elementary G-biliaisons of height to an ideal of indeterminates and, conversely, that every G-biliaison of a certain type gives rise to a geometric vertex decomposition. As a consequence, we can immediately conclude that several well-known families of ideals are glicci, including Schubert determinantal ideals, defining ideals of varieties of complexes and defining ideals of graded lower bound cluster algebras.

Original language | English (US) |
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Article number | e70 |

Journal | Forum of Mathematics, Sigma |

Volume | 9 |

DOIs | |

State | Published - Oct 19 2021 |

Externally published | Yes |

### Bibliographical note

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## Keywords

- Geometric vertex decomposition
- Gröbner bases
- Gröbner degeneration
- Liaison
- Linkage