Apparaît dans la collection : The Ubiquity of Commutative Algebra / Ubiquité de l'algèbre commutative

Geometric vertex decomposition was introduced by Knutson, Miller, and Yong in the study of the Groebner geometry of matrix Schubert varieties. It extends vertex decomposition for simplicial complexes to algebraic varieties and polynomial ideals, providing an inductive strategy for reducing questions to simpler pieces. Frobenius splitting studies singularities in positive characteristic. Knutson showed that Frobenius splittings descend through geometric vertex decomposition to the link and deletion. We define these ideas and present joint work with De Negri, Klein, Rajchgot, and Seccia establishing a partial converse.