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Families of Gröbner degenerations
Algebraic Geometry| Speaker: | Lara Bossinger, Instituto de Matemáticas |
| Related Webpage: | https://www.matem.unam.mx/~lara/ |
| Location: | Zoom |
| Start time: | Wed, May 11 2022, 2:10PM |
In this talk, we will treat the following motivating question: given a projective variety X is it possible to classify all its toric degeneration (flat families that contain X as a generic fiber and a projective toric variety as a special fiber). Through a sequence of structural results, we may restrict our attention to Gröbner degenerations of X and analyze families that contain more than one toric fiber. The construction yields interesting applications in cluster algebras which I will illustrate in the examples of the Grassmannians Gr(2,n) and Gr(3,6) (based on joint work with Fatemeh Mohammado and Alfredo Nájera Chávez).