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Thomas Kahle : Toric Fiber Products

The toric fiber product is a general procedure for gluing two ideals, homogeneous with respect to the same grading, to produce a new homogeneous ideal. Toric fiber products generalize familiar constructions in commutative algebra like adding monomial ideals and the Segre product. We will introduce the construction, discuss its geometrical content, and give an overview over the various preserved properties. Toric fiber products have been applied most successfully to families of ideals parametrized by combinatorial objects like graphs. We will show how to use toric fiber product to prove structural theorems about classes of ideals from algebraic statistics.

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