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## Combinatorics of F-polynomials

༭wfy ʱ䣺20191118 ʴ:297

ĿCombinatorics of F-polynomials

ˣѼ оԱ Ϻͨѧ

rg20191126ڶ10:00_ʼ

cȪУ^̘200-9

Abstract

We introduce the stabilization functors to study the combinatorial aspect of the F-polynomial of a representation of any finite-dimensional basic algebra.

The F-polynomial of a quiver representation M is the generating series of the topological Euler characteristic of the representation Grassmannian of M:

F_M(y) = \sum_{\gamma} \chi(Gr_\gamma(M))y^\gamma.

We characterize the vertices of their Newton polytopes. We give an explicit formula for the F-polynomial restricting to any face of its Newton polytope.

For acyclic quivers, we give a complete description of all facets of the Newton polytope when the representation is general. We also prove that the support of F-polynomial is saturated for any rigid representation. We provide many examples and counterexamples, and pose several conjectures.

˼飺2010ЪѧʿѧλʦHarm Derksen漴ڼݴѧӱУη4꣬ڼMSRIоԱ£̨֮ۿѧĵоԱꡣ2017ϺͨѧرоԱҸ߲˲Ŀ֧֡

MҪоIڱʾՓwоdȤDʾՓͲ׃Փ

ϵˣ(fangli@zju.edu.cn)