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تسجيل مستخدم جديدK-moduli of curves on a quadric surface and K3 surfaces
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We show that the K-moduli spaces of log Fano pairs $(mathbb{P}^1timesmathbb{P}^1, cC)$ 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-OGrady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of $(4,4)$-curves on $mathbb{P}^1timesmathbb{P}^1$ and the Baily-Borel compactification of moduli of quartic hyperelliptic K3 surfaces.
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We show that the K-moduli spaces of log Fano pairs $(mathbb{P}^3, cS)$ 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 surfaces as $c$ varies in
the interval $(0,1)$. We completely describe the wall crossings of these K-moduli spaces. As the main application, we verify Laza-OGradys prediction on the Hassett-Keel-Looijenga program for quartic K3 surfaces. We also obtain the K-moduli compactification of quartic double solids, and classify all Gorenstein canonical Fano degenerations of $mathbb{P}^3$.
Let $F$ be a moduli space of lattice-polarized K3 surfaces. Suppose that one has chosen a canonical effective ample divisor $R$ on a general K3 in $F$. We call this divisor recognizable if its flat limit on Kulikov surfaces is well defined. We prove
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We study the virtual geometry of the moduli spaces of curves and sheaves on K3 surfaces in primitive classes. Equivalences relating the reduced Gromov-Witten invariants of K3 surfaces to characteristic numbers of stable pairs moduli spaces are proven
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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
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