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Sang-Bum Yoo

Publications and source records attributed to Sang-Bum Yoo.

12 recordsLinked to original sources
arXiv2026

Infinitesimal automorphisms and obstruction theory on the moduli of $L$-valued $G$-Higgs bundles

For an arbitrary reductive group $G$, we compute the infinitesimal automorphisms of $L$-valued principal $G$-Higgs bundles over a compact Kähler manifold $X$, extending known results for $Ω_X^{1}$-valued $G$-Higgs bundles. Using this computation, when $G$ is semisimple and $X$ is a smooth projective variety, we show that the moduli stack of stable $L$-valued $G$-Higgs bundles is a Deligne-Mumford (DM) stack. Furthermore, when $X$ is a smooth projective surface and $L=K_X$, we construct a symmetric perfect obstruction theory on this stable locus. We expect this will provide a foundation for defining Vafa-Witten invariants for reductive groups $G$.

math.AG↗
arXiv2026

A chain of $\mathbb{C}^{*}$-flips of the moduli spaces of $\mathcal{O}$-twisted rank 2 constrained framed Hitchin pairs on a smooth curve

Let $X$ be a smooth complex projective curve. We prove that there exists a surjective commutative forgetful diagram from the chain of $\mathbb{C}^{*}$-flips of the moduli spaces of $\mathcal{O}_{X}$-twisted rank 2 constrained framed Hitchin pairs on $X$ to the chain of $\mathbb{C}^{*}$-flips of the moduli spaces of rank 2 framed modules on $X$.

math.AG↗
arXiv2025

Virtual Poincare polynomial of moduli space of semistable sheaves of rank two on reducible curves

The main purpose of this paper is to give an explicit description of the moduli space of semistable sheaves of rank two on a stable curve C obtained by gluing two smooth curves at a point. We prove that the moduli space is irreducible and birational to a projective bundle over the moduli space of stable vector bundles on each component curve, independently of the choice of polarization. As an application, we compute the virtual Poincare polynomial of the moduli space.

math.AG↗
arXiv2025

Rational curves in a quadric threefold via an $\text{SL}(2,\mathbb{C})$-representation

In this paper, we regard the smooth quadric threefold $Q_{3}$ as Lagrangian Grassmannian and search for fixed rational curves of low degree in $Q_{3}$ with respect to a torus action, which is the maximal subgroup of the special linear group $\text{SL}(2,\mathbb{C})$. Most of them are confirmations of very well-known facts. If the degree of a rational curve is $3$, it is confirmed using the Lagrangian's geometric properties that the moduli space of twisted cubic curves in $Q_3$ has a specific projective bundle structure. From this, we can immediately obtain the cohomology ring of the moduli space.

math.AG↗
arXiv2021

A desingularization of the moduli space of rank 2 Higgs bundles over a curve

Let $X$ be a smooth complex projective curve of genus $g\geq 3$. Let $\mathbf{M}_2$ be the moduli space of semistable rank $2$ Higgs bundles with trivial determinant over $X$. We construct a desingularization $\mathbf{S}$ of $\mathbf{M}_2$ as a closed subvariety of a moduli space. We prove that $\mathbf{S}$ is a nonsingular variety containing the stable locus of $\mathbf{M}_2$ as an open dense subvariety. On the other hand, there is another desingularization $\mathbf{K}$ of $\mathbf{M}_2$ obtained from Kirwan's algorithm. We show that $\mathbf{S}$ can be obtained after two blow-downs of $\mathbf{K}$.

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arXiv2021

Hecke cycles associated to rank 2 twisted Higgs bundles on a curve

Let $X$ be a smooth complex projective curve of genus $g$ and let $L$ be a line bundle on $X$ with $\mathrm{deg}\,L>0$. Let $\mathbf{M}$ be the moduli space of semistable rank 2 $L$-twisted Higgs bundles with trivial determinant on $X$. Let $\mathbf{M}_{X}$ be the moduli space of stable rank 2 $L$-twisted Higgs bundles with determinant $\mathcal{O}(-x)$ for some $x\in X$ on $X$. We construct a cycle in the product of a stack of rational maps from nonsingular curves to $\mathbf{M}_{X}$ and $\mathrm{Pic}^{2\mathrm{deg}\,L}(X)$ by using Hecke modifications of a stable $L$-twisted Higgs bundle in $\mathbf{M}$.

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arXiv2019

Finite generation of the algebra of type A conformal blocks via birational geometry II: higher genus

We prove finite generation of the algebra of type A conformal blocks over arbitrary stable curves of any genus. As an application we construct a flat family of irreducible normal projective varieties over the moduli stack of stable pointed curves, whose fiber over a smooth curve is a moduli space of semistable parabolic bundles. This generalizes a construction of a degeneration of the moduli space of vector bundles presented in a recent work of Belkale and Gibney.

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arXiv2017

Finite generation of the algebra of type A conformal blocks via birational geometry

We study birational geometry of the moduli space of parabolic bundles over a projective line, in the framework of Mori's program. We show that the moduli space is a Mori dream space. As a consequence, we obtain the finite generation of the algebra of type A conformal blocks. Furthermore, we compute the H-representation of the effective cone which was previously obtained by Belkale. For each big divisor, the associated birational model is described in terms of moduli space of parabolic bundles.

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