Related papers: Non-proportional wall crossing for K-stability

An arrangement of k-semilines in the Euclidean (projective) plane or on the 2-sphere is called a k-fan if all semilines start from the same point. A k-fan is an $\alpha$-partition for a probability measure $\mu$ if $\mu(\sigma_i)=\alpha_i$…

We study a natural family of non-local elliptic boundary problems on a compact oriented surface $\Sigma$ parametrized by the moduli space $\mathcal{M}_\Sigma$ of flat $G$-connections with framing along $\partial \Sigma$. This family…

We propose a framework to construct "Domain-Wall Standard Model" in a non compact 5-dimensional space-time, where all the Standard Model (SM) fields are localized in certain domains of the 5th dimension and the SM is realized as a…

We consider normal projective n-dimensional varieties X whose anticanonical divisor class -K is ample and where every Weil divisor is a rational multiple of K. The index i is the largest integer such that K/i exists as a Weil divisor. We…

We study the K-moduli stack of prime Fano threefolds of genus twelve, known as $V_{22}$. We prove that its boundary, which parametrizes singular members, is purely divisorial and consists of four irreducible components corresponding to the…

We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on…

For every integer $a \geq 2$, we relate the K-stability of hypersurfaces in the weighted projective space $\mathbb{P}(1,1,a,a)$ of degree $2a$ with the GIT stability of binary forms of degree $2a$. Moreover, we prove that such a…

We study genus zero wall-crossing for a family of moduli spaces introduced recently by Fan-Farvis-Ruan. The family has a wall and chamber structure relative to a positive rational parameter. For a Fermat quasi-homogeneous polynomial W (not…

We study the complex-analytic geometry of semi-positive holomorphic line bundles on compact K\"ahler manifolds. In one of our main results, for a $\mathbb{Q}$-effective line bundle satisfying a natural torsion-type assumption, we show the…

1) Assuming log Minimal Model Conjecture, we give a construction of a complete moduli space of stable log pairs of arbitrary dimension generalizing directly the space M_{g,n} of pointed stable curves. Each stable pair has semi log canonical…

We give a characterization of K-g-fusion frames and discuss the stability of dual g-fusion frames. We also present a necessary and sufficient condition for a quotient operator to be bounded.

We introduce a notion of Gieseker stability for coherent sheaves on tame Deligne-Mumford stacks with projective moduli scheme and some chosen generating sheaf on the stack in the sense of Olsson and Starr \cite{MR2007396}. We prove that…

We give a log-geometric description of the space of twisted canonical divisors constructed by Farkas--Pandharipande. In particular, we introduce the notion of a principal rubber $k$-log-canonical divisor, and we study its moduli space. It…

We prove a rigidity result for automorphisms of points of certain stacks admitting adequate moduli spaces. It encompasses as special cases variations of the moduli of $G$-bundles on a smooth projective curve for a reductive algebraic group…

Currently, much interest is drawn to the analysis of optical and matter-wave modes supported by the fractional diffraction in nonlinear media. We predict a new type of such states, in the form of domain walls (DWs) in the two-component…

We prove some criteria for uniform K-stability of log Fano pairs. In particular, we show that uniform K-stability is equivalent to $\beta$-invariant having a positive lower bound. Then we study the relation between optimal destabilization…

We prove a quantum version of Kalkman's wall-crossing formula comparing Gromov-Witten invariants on geometric invariant theory (git) quotients related by a change in polarization. The wall-crossing terms are gauged Gromov-Witten invariants…

In this paper we set up the family Seiberg-Witten theory. It can be applied to the counting of nodal pseudo-holomorphic curves in a symplectic 4-manifold (especially a Kahler surface). A new feature in this theory is that the chamber…

We present a new calculation of the K->pi semileptonic form factor at zero momentum transfer in domain wall lattice QCD with Nf=2+1 dynamical quark flavours. By using partially twisted boundary conditions we simulate directly at the…

In this paper, we prove a K-theoretic wall-crossing formula for $\epsilon$-stable quasimaps for all GIT targets in all genera. It recovers the genus-0 K-theoretic toric mirror theorem by Givental-Tonita and the genus-0 mirror theorem for…