Families of Gröbner degenerations

Abstract: In this talk I will present a construction of one flat family that combines many Gröbner degenerations. More precisely, for a (weighted) homogeneous ideal we consider a maximal cone in its Gröbner fan. Associated to that cone we define a flat family that contains various special fibers associated to the initial degenerations of the cone and all its faces. This construction has several interesting applications. Most surprisingly, it recovers the recursive construction of universal coefficients for cluster algebras in a non-recursive way for the Grassmannians Gr(2,n) and Gr(3,6). If time permits I will present another application explaining how to recover Kaveh-Manon's toric equivariant families arising from a collection of nice cones in the tropicalization of an ideal. This talk is based on joint work in progress with F. Mohammadi and A. Nájera Chávez.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides | video )

---

Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).

Videos of the talks can be viewed here.

Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.

---