Related papers: K-moduli with real coefficients

This is essentially an expository note based on S. Paul's works on the stability of pairs. Its connection to K-stability will be also discussed.

We propose a new type of K\"ahler moduli stabilization mechanisms in type IIB superstring theory on Calabi-Yau manifolds with the positive Euler number. The overall K\"ahler modulus can be perturbatively stabilized by radiative corrections…

A C*-algebra is said to be K-stable if its nonstable K-groups are naturally isomorphic to the usual K-theory groups. We study continuous $C(X)$-algebras, each of whose fibers are K-stable. We show that such an algebra is itself K-stable…

We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(S^n x S^n), provided n > 2. This generalises Harer's stability theorem for the homology of mapping class groups. Combined with previous work of…

Let $(X,\mathcal{O}_X(1))$ be a polarized smooth projective variety over the complex numbers. Fix $\mathcal{D}\in \mathrm{coh}(X)$ and a nonnegative rational polynomial $\delta$. Using GIT we contruct a coarse moduli space for…

We interpret the coupled Ding semistability and the reduced coupled uniform Ding stability of log Fano pairs in the notion of coupled stability thresholds and reduced coupled stability thresholds. As a corollary, we solve a modified version…

We analyze the classical stability of Q-tubes --- charged extended objects in $(3+1)$-dimensional complex scalar field theory. Explicit solutions were found analytically in the piecewise parabolic potential. Our choice of potential allows…

We study K-stability of smooth Fano threefolds of Picard rank $2$ and degree $22$ which can be obtained by blowing up a smooth complete intersection of two quadrics in $\mathbb{P}^5$ along a conic. We also describe the automorphism groups…

We give an algebraic proof for which log del Pezzo pairs of Maeda type are K-polystable or not. If the base field is the complex number field, then the result is already known by Li and Sun.

To any projective pair $(X,B)$ equipped with an ample $\mathbb{Q}$-line bundle $L$ (or even any ample numerical class), we attach a new invariant $\beta(\mu)\in\mathbb{R}$, defined on convex combinations $\mu$ of divisorial valuations on…

Motivated by the study of Fano type varieties we define a new class of log pairs that we call asymptotically log Fano varieties and strongly asymptotically log Fano varieties. We study their properties in dimension two under an additional…

For a variety $X$, a big $\mathbb{Q}$-divisor $L$ and a closed connected subgroup $G \subset \mathrm{Aut}(X, L)$ we define a $G$-invariant version of the $\delta$-threshold. We prove that for a Fano variety $(X, -K_X)$ and a connected…

We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a $\Theta$-stratification. These results provide a…

Let $N$ be a normal subgroup of a group $G$. An $N$-module $Q$ is $G$-stable provided that $Q$ is equivalent to the twist $Q^g$ of $Q$ by $g$, for every $g\in G$. If the action of $N$ on $Q$ extends to an action of $G$ on $Q$, $Q$ is…

We give a parametrization of test configurations in the sense of Donaldson via spherical buildings, and show the existence of "optimal" destabilizing test configurations for unstable varieties, in the wake of Mumford and Kempf. We also give…

We study moduli stabilization by thermal effects in the cosmological context. The implementation of finite temperature, which spontaneously breaks supersymmetry, induces an effective potential at one loop level. At the points where extra…

We study moduli stabilization in the context of M-theory on compact manifolds with G2 holonomy, using superpotentials from flux and membrane instantons, and recent results for the Khaeler potential of such models. The existence of minima…

We prove a motivic stabilization result for the cohomology of the local systems on configuration spaces of varieties over $\mathbb{C}$ attached to character polynomials. Our approach interprets the stabilization as a probabilistic…

Let X be a Fano manifold. G.Tian proves that if X admits a Kaehler-Einstein metric, then it satisfies two different stability conditions: one involving the Futaki invariant of a special degeneration of X, the other Hilbert-Mumford-stability…

We exhibit an example of obstructed K-polystable Fano 3-fold $X$ such that the K-moduli stack of K-semistable Fano varieties and the K-moduli space of K-polystable Fano varieties have an embedded point at $[X]$.