相关论文: Crossing the Wall: Branes vs. Bundles

We shall study the wall crossing behavior of moduli of stable sheaves on an elliptic surface.

We study the moduli spaces of surface pairs $(X,D)$ admitting a log Calabi--Yau fibration $(X,D) \to C$. We develop a series of results on stable reduction and apply them to give an explicit description of the boundary of the KSBA…

Recently, Oh and Thomas constructed algebraic virtual cycles for moduli spaces of sheaves on Calabi-Yau 4-folds. The purpose of this paper is to provide a virtual pullback formula between these Oh-Thomas virtual cycles. We find a natural…

We construct a statistical model that correctly reproduces the BPS partition function of D4-D2-D0 bound states on the resolved conifold. We prove that the known partition function of the BPS indices is reproduced by the counting "triangular…

Let $\mathbf{M}_d$ be the moduli space of stable sheaves on $\mathbb{P}^2$ with Hilbert polynomial $dm+1$. In this paper, we determine the effective and the nef cone of the space $\mathbf{M}_d$ by natural geometric divisors. Main idea is to…

We study the BPS spectrum of four-dimensional $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group $SU(2)$ and a massive adjoint hypermultiplet, which has an extremely intricate structure with infinite spectrum in all chambers…

We construct proper good moduli spaces parametrizing K-polystable $\mathbb{Q}$-Gorenstein smoothable log Fano pairs $(X, cD)$, where $X$ is a Fano variety and $D$ is a rational multiple of the anti-canonical divisor. We then establish a…

In this work, we provide evidence for a duality between 4-dimensional Calabi-Yau compactifications of the heterotic string, in which the base manifolds are linked by a conifold transition. In recent work, a geometric proposal was put…

We describe physical phenomena associated with a class of transitions that occur in the study of supersymmetric three-cycles in Calabi-Yau threefolds. The transitions in question occur at real codimension one in the complex structure moduli…

We study projectivity of moduli spaces on the DT/PT wall crossing in Bridgeland and polynomial stability on a smooth, projective threefold. First, we construct a globally generated line bundle on the moduli stack of higher-rank…

We give a summary of a talk delivered at the 2012 International Congress on Mathematical Physics. We review d=4, N=2 quantum field theory and some of the exact statements which can be made about it. We discuss the wall-crossing phenomenon.…

The invariants of rank 2 Joyce-Song semistable pairs over a Calabi-Yau threefold were computed in arXiv:1101.2252, using the wall-crossing formula of Joyce-Song and Kontsevich-Soibelman. Such wall-crossing computations often depend on the…

We study normal functions capturing D-brane superpotentials on several one- and two-parameter Calabi-Yau hypersurfaces and complete intersections in weighted projective space. We calculate in the B-model and interpret the results using…

Recently, using supergravity analysis, a hyperbolic reflection group was found to underlie the structure of wall-crossing, or the discontinuous moduli dependence of the supersymmetric index due to the presence of walls of marginal…

In this paper, we introduce the notion of parabolic stable pairs on Calabi-Yau 3-folds and invariants counting them. By applying the wall-crossing formula developed by Joyce-Song, Kontsevich-Soibelman, we see that they are related to…

We prove, under suitable conditions, that there exist wall-crossing and reduction morphisms for moduli spaces of stable log pairs in all dimensions as one varies the coefficients of the divisor.

This paper studies wall crossings in Bridgeland stability for the moduli space of Pandharipande--Thomas stable pairs associated with quintic genus 2 curves in the complex projective three-space. We provide a complete list of irreducible…

BPS states in N=4 supersymmetric SU(N) gauge theories in four dimensions can be represented as planar string networks with ends lying on D3-branes. We introduce several protected indices which capture information on the spectrum and various…

We study birational maps among 1) the moduli space of semistable torsion sheaves of Hilbert polynomial $4m+2$ on a smooth quadric surface, 2) the moduli space of semistable torsion sheaves of Hilbert polynomial $m^{2}+3m+2$ on…

We provide a wall-crossing framework for operational enumerative invariants of equivariant 3-Calabi--Yau categories arising from virtual cycles. The strategy follows ideas of Joyce's ``universal'' wall-crossing framework arXiv:2111.04694,…