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Abstract: Geometric vertex decomposition (a degeneration technique) and liaison are two frameworks that have been used to produce similar results about similar families of algebraic varieties. In this talk, I will describe an explicit connection between these two approaches. In particular, I will show that each geometrically vertex decomposable ideal is linked by a sequence of ascending elementary G-biliaisons of height 1 to an ideal of indeterminates and, conversely, that each elementary G-biliaison of a certain type gives rise to a geometric vertex decomposition.
After explaining this connection, I'll discuss some applications including (i) showing that several well-known families of ideals are (automatically) glicci, (ii) obtaining a framework for implementing, with relative ease, Gorla, Migliore, and Nagel’s strategy of using liaison to establish Gr\"obner bases, and (iii) using geometric vertex decomposition to answer a question of Nagel and Romer from their study of liaison and squarefree monomial ideals.
The first half of the talk will focus on background and motivation, and the second half will be on the above-mentioned work, which is joint with Patricia Klein.No Notes/Supplements Uploaded No Video Files Uploaded