Kenneth Ascher

Wall crossing for K-moduli spaces of plane curves

arXiv (Cornell University) · 2019-09-10 · 20 citations

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 wall-crossing framework of these K-moduli spaces as $c$ varies. The main application in this paper is the case of plane curves of degree $d \geq 4$ as boundary divisors of $\mathbb{P}^2$. In this case, we show that when the coefficient $c$ is small, the K-moduli…

K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES

Journal of the Institute of Mathematics of Jussieu · 2021 · 15 citations

Abstract We show that the K-moduli spaces of log Fano pairs $\left(\mathbb {P}^1\times \mathbb {P}^1, cC\right)$ , where C is a $(4,4)$ curve and their wall crossings coincide with the VGIT quotients of $(2,4)$ , complete intersection curves in $\mathbb {P}^3$ . This, together with recent results by Laza and O’Grady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of $(4,4)$ curves on $\mathbb {P}^1\times \mathbb {P}^1$ and the Baily–Borel compactific…

K-stability and birational models of moduli of quartic K3 surfaces

Inventiones mathematicae · 2022 · 14 citations

Abstract We show that the K-moduli spaces of log Fano pairs $$({\mathbb {P}}^3, cS)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msup><mml:mo>,</mml:mo><mml:mi>c</mml:mi><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> where S is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily–Borel compactification of moduli of quartic K3 surfa…

Compact moduli of elliptic K3 surfaces

Geometry & Topology · 2023 · 12 citations

We construct various modular compactifications of the space of elliptic K3 surfaces using tools from the minimal model program, and explicitly describe the surfaces parametrized by their boundaries.The coarse spaces of our constructed compactifications admit morphisms to the Satake-Baily-Borel compactification and the GIT compactification of Miranda.

Wall crossing for K‐moduli spaces of plane curves

Proceedings of the London Mathematical Society · 2024-06-01 · 8 citations

Abstract We construct proper good moduli spaces parametrizing K‐polystable ‐Gorenstein smoothable log Fano pairs , where is a Fano variety and is a rational multiple of the anticanonical divisor. We then establish a wall‐crossing framework of these K‐moduli spaces as varies. The main application in this paper is the case of plane curves of degree as boundary divisors of . In this case, we show that when the coefficient is small, the K‐moduli space of these pairs is isomorphic to the GIT moduli s…