Related papers: Wall crossing for K-moduli spaces of plane curves

Let $\mathbf{M}^{\alpha}(d,\chi)$ be the moduli space of $\alpha$-stable pairs $(s,F)$ on the projective plane $\mathbb{P}^2$ with Hilbert polynomial $\chi(F(m))=dm+\chi$. For sufficiently large $\alpha$ (denoted by $\infty$), it is well…

For every genus g, we construct a smooth, complete, rational polarized algebraic variety DM_g together with a normal crossing divisor D = sum D_i, such that for every moduli space M_C(2,0) of semistable topologically trivial vector bundles…

The 'moduli continuity method' permits an explicit algebraisation of the Gromov-Hausdorff compactification of K\"ahler-Einstein metrics on Fano manifolds in some fundamental examples. In this paper, we apply such method in the 'log setting'…

In this paper, we consider the CM line bundle on the K-moduli space, i.e., the moduli space parametrizing K-polystable Fano varieties. We prove it is ample on any proper subspace parametrizing reduced uniformly K-stable Fano varieties which…

We give a natural family of Bridgeland stability conditions on the derived category of a smooth projective complex surface S and describe ``wall-crossing behavior'' for objects with the same invariants as $\cO_C(H)$ when H generates Pic(S)…

We show that the Hilbert scheme of curves and Le Potier's moduli space of stable pairs with one dimensional support have a common GIT construction. The two spaces correspond to chambers on either side of a wall in the space of GIT…

We explicitly describe the KSBA/Hacking compactification of a moduli space of log surfaces of Picard rank 2. The space parametrizes log pairs $(S, D)$ where $S$ is a degeneration of $\mathbb{P}^1 \times \mathbb{P}^1$ and $D \subset S$ is a…

We study the wall-crossing for moduli spaces of coherent systems of dimension one and order one on a smooth projective variety over the complex numbers. We compute the topological Euler characteristic of the moduli spaces in the particular…

Inspired by the log Gromov-Witten (or GW) theory of Gross-Siebert/Abramovich-Chen, we introduce a geometric notion of log J-holomorphic curve relative to a simple normal crossings symplectic divisor defined in [FMZ1]. Every such moduli…

Motivated by the relation between (twisted) K3 surfaces and special cubic fourfolds, we construct moduli spaces of polarized twisted K3 surfaces of any fixed degree and order. We do this by mimicking the construction of the moduli space of…

S. Kondo has constructed a ball quotient compactification for the moduli space of non-hyperelliptic genus four curves. In this paper, we show that this space essentially coincides with a GIT quotient of the Chow variety of canonically…

We give a new proof of Ciocan-Fontanine and Kim's wall-crossing formula relating the virtual classes of the moduli spaces of $\epsilon$-stable quasimaps for different $\epsilon$ in any genus, whenever the target is a complete intersection…

In this note, we prove two results regarding the variation of K-moduli. The first one reveals the relationship between the chamber decomposition for K-semistable domains and the variation of GIT. The second one presents the relationship…

We test a recently proposed wall-crossing formula for the change of the Hilbert space of BPS states in d=4,N=2 theories. We study decays of D4D2D0 systems into pairs of D4D2D0 systems and we show how the wall-crossing formula reproduces…

We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable Fano varieties. Specifically, we prove that if the stability…

We extend the ideas of Friedman and Qin (Flips of moduli spaces and transition formulae for Donaldson polynomial invariants of rational surfaces) to find the wall-crossing formulae for the Donaldson invariants of algebraic surfaces with…

We state a wall-crossing formula for the virtual classes of epsilon-stable quasimaps to GIT quotients and prove it for complete intersections in projective space, with no positivity restrictions on their first Chern class. As a consequence,…

We construct geometric compactifications of the moduli space $F_{2d}$ of polarized K3 surfaces, in any degree $2d$. Our construction is via KSBA theory, by considering canonical choices of divisor $R\in |nL|$ on each polarized K3 surface…

The extension from toric varieties to quantum toric stacks allows for the study of moduli spaces of toric objects with fixed combinatorial structures, as we now consider general finitely generated subgroups of $\mathbb{R}^n$ as "lattices."…

In this paper, we study the moduli space of quasi-polarized complex K3 surfaces of degree 6 and 8 via geometric invariant theory. The general members in such moduli spaces are complete intersections in projective spaces and we have natural…