8 papers · 1 filter
Cohomology of moduli spaces of pointed curves
Jinwon Choi, Young-Hoon Kiem
In this paper, after reviewing recent progress on the cohomology of , we further our investigation on the cohomology of moduli spaces of pointed curves in…
Stratified motivic invariants and bivariate deformations of Poincaré polynomials
Gergely Bérczi, Young-Hoon Kiem
For a stratified variety and a motivic invariant , we consider the stratified invariant which interpolates the invariant of and that of its interior …
Real-rootedness of the Poincaré polynomials of : an AI-assisted proof
Gergely Bérczi, Young-Hoon Kiem
We prove real-rootedness for the Poincaré polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne--Mumford moduli space $\ov…
Asymptotic distribution of the Betti numbers of
Jinwon Choi, Young-Hoon Kiem
Asymptotic normality is frequently observed in large combinatorial structures, rigorously established for many quantities such as cycles or inversions in random permutations, the n…
Generalized intersection pairings on moduli spaces of vector bundles over a curve
Chenjing Bu, Young-Hoon Kiem
We introduce the notion of a generalized intersection pairing for an Artin stack with a proper good moduli space and nonempty stable part. For the moduli stack of semistable bundle…
Characteristic polynomial of and log-concavity
Jinwon Choi, Young-Hoon Kiem, Donggun Lee
Motivated by Stanley's generalization of the chromatic polynomial of a graph to the chromatic symmetric function, we introduce the characteristic polynomial of a representation of…