115 citations · 707 across the 84 of their papers we have counts for
50 papers · 1 filter
Hodge-Deligne and Poincaré polynomials of
Young-Hoon Kiem
By studying wall crossings of Hassett moduli spaces of weighted pointed curves, we prove a recursive formula that reduces the computation of the cohomology of $\overline{\mathcal M…
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 $\ove…
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…
Cosection localization via shifted symplectic geometry
Young-Hoon Kiem, Hyeonjun Park
The purpose of this paper is to shed a new light on classical constructions in enumerative geometry from the view point of derived algebraic geometry. We first prove that the cosec…
Recursive algorithm and log-concavity of representations on the cohomology of
Jinwon Choi, Young-Hoon Kiem, Donggun Lee
We provide a programmable recursive algorithm for the -representations on the cohomology of the moduli spaces of -pointed stable curv…
Geometry of the twin manifolds of regular semisimple Hessenberg varieties and unicellular LLT polynomials
Young-Hoon Kiem, Donggun Lee
Recently, Masuda-Sato and Precup-Sommers independently proved an LLT version of the Shareshian-Wachs conjecture which says that the Frobenius characteristics of the cohomology of t…
Birational geometry of generalized Hessenberg varieties and the generalized Shareshian-Wachs conjecture
Young-Hoon Kiem, Donggun Lee
We introduce generalized Hessenberg varieties and establish basic facts. We show that the Tymoczko action of the symmetric group on the cohomology of Hessenberg varieties ext…
Representations on the cohomology of
Jinwon Choi, Young-Hoon Kiem, Donggun Lee
The moduli space of pointed stable curves of genus admits an action of the symmetric group by permuting the marked points. We provide a…
Localizing virtual cycles for Donaldson-Thomas invariants of Calabi-Yau 4-folds
Young-Hoon Kiem, Hyeonjun Park
Recently Oh-Thomas constructed a virtual cycle for a quasi-projective moduli space of stable sheaves or complexes over a Calabi-Yau 4-fold agains…
Localizing Virtual Structure Sheaves for Almost Perfect Obstruction Theories
Young-Hoon Kiem, Michail Savvas
Almost perfect obstruction theories were introduced in an earlier paper by the authors as the appropriate notion in order to define virtual structure sheaves and -theoretic inva…
K-Theoretic Generalized Donaldson-Thomas Invariants
Young-Hoon Kiem, Michail Savvas
We introduce the notion of almost perfect obstruction theory on a Deligne-Mumford stack and show that stacks with almost perfect obstruction theories have virtual structure sheaves…
Virtual intersection theories
Young-Hoon Kiem, Hyeonjun Park
We construct virtual fundamental classes in all intersection theories including Chow theory, K-theory and algebraic cobordism for quasi-projective Deligne-Mumford stacks with perfe…
Algebraic virtual cycles for quantum singularity theories
Huai-Liang Chang, Young-Hoon Kiem, Jun Li
We construct algebraic virtual cycles that give us the cohomological field theories of Fan-Jarvis-Ruan invariants by integral transformations.
Quantum singularity theory via cosection localization
Young-Hoon Kiem, Jun Li
We generalize the cosection localized Gysin map to intersection homology and Borel-Moore homology, which provides us with a purely topological construction of the Fan-Jarvis-Ruan-W…
Generalized Donaldson-Thomas Invariants via Kirwan Blowups
Young-Hoon Kiem, Jun Li, Michail Savvas
We develop a virtual cycle approach towards generalized Donaldson-Thomas theory of Calabi-Yau threefolds. Let be the moduli stack of Gieseker semistable sheaves of fi…
Localizing virtual structure sheaves by cosections
Young-Hoon Kiem, Jun Li
We construct a cosection localized virtual structure sheaf when a Deligne-Mumford stack is equipped with a perfect obstruction theory and a cosection of the obstruction sheaf.
Localizing virtual fundamental cycles for semi-perfect obstruction theories
Young-Hoon Kiem
Recently H.-L. Chang and J. Li generalized the theory of virtual fundamental class to the setting of semi-perfect obstruction theory. A semi-perfect obstruction theory requires onl…
All complete intersection varieties are Fano visitors
Young-Hoon Kiem, In-Kyun Kim, Hwayoung Lee +1
We prove that the derived category of a smooth complete intersection variety is equivalent to a full subcategory of the derived category of a smooth projective Fano variety. This e…
Fano visitors, Fano dimension and orbifold Fano hosts
Young-Hoon Kiem, Kyoung-Seog Lee
In arXiv:1503.00125, the authors proved that every complete intersection smooth projective variety is a Fano visitor, i.e. its derived category is equivalent to a full…
Torus localization and wall crossing for cosection localized virtual cycles
Huai-Liang Chang, Young-Hoon Kiem, Jun Li
Since its introduction in 1995 by Li-Tian and Behrend-Fantechi, the theory of virtual fundamental class has played a key role in algebraic geometry, defining important invariants s…