Geometric vertex decomposition and liaison

Geometric vertex decomposition and liaison are two frameworks that have been used to produce similar results about families of algebraic varieties. In this paper, we establish an explicit connection between these approaches. particular, show each geometrically decomposable ideal is linked by a sequence elementary G-biliaisons height 1 indeterminates and, conversely, every G-biliaison certain type gives rise geometric decomposition. As consequence, can immediately conclude several well-known ideals glicci, including Schubert determinantal ideals, defining varieties complexes, graded lower bound cluster algebras.