相关论文: K-stability of log del Pezzo hypersurfaces with in…

We introduce the notion of strongly asymptotically log del Pezzo flags, and classify such flags under the assumption that their zero-dimensional part lies in the boundary. We use this result to give a new and conceptual proof of the…

We study points and 0-cycles on del Pezzo surfaces defined over a field K of characteristic 0, with emphasis on cubic surfaces. We prove that a cubic surface that admits a point defined over a field extension of K of degree coprime to 3…

Any minimal Del Pezzo G-surface S of degree smaller than 3 is G-birationally rigid. We classify those which are G-birationally superrigid and for those which fail to be so, we describe the equations of a set of generators for the infinite…

The delta invariant interprets the criterion for the K-(poly)stability of log terminal Fano varieties. In this paper, we determine the whole local delta invariant for all weak del Pezzo surfaces with the anti-canonical degree $\geq 5$.

We determine the complete list of anticanonically embedded quasi smooth log del Pezzo surfaces in weighted projective 3-spaces. We prove that many of these admit a K\"ahler-Einstein metric and most of them do not have tigers.

We make some observation on the logarithmic version of K-stability.

We prove K-stability for infinitely many smooth members of the family 2.19 of the Mukai-Mori classification.

We consider two classes of non-toric log del Pezzo $\mathbb{C}^*$-surfaces: on the one side the 1/3-log canonical ones and on the other side those of Picard number one and Gorenstein index at most 65. In each of the two classes we figure…

Let $G$ be a finite group and $H\subseteq G$ be its subgroup. We prove that if a smooth del Pezzo surface over an algebraically closed field is $H$-birationally rigid then it is also $G$-birationally rigid, answering a geometric version of…

The K-moduli theory provides a different compactification of moduli spaces of curves. As a general genus six curve can be canonically embedded into the smooth quintic del Pezzo surface, we study in this paper the K-moduli spaces…

This paper focuses on the classification of all toric log Del Pezzo surfaces with exactly one singularity up to isomorphism, and on the description of how they are embedded as intersections of finitely many quadrics into suitable projective…

We study the geometry of stable maximal hypersurfaces in a variety of spacetimes satisfying various physically relevant curvature assumptions, for instance the Timelike Convergence Condition (TCC). We characterize stability when the target…

We show that certain Galois covers of K-semistable Fano varieties are K-stable. We use this to give some new examples of Fano manifolds admitting K\"ahler-Einstein metrics, including hypersurfaces, double solids and threefolds.

We classify all log del Pezzo surfaces of Picard number one defined over algebraically closed fields of characteristic different from two and three. We also discuss some consequences of the classification. For example, we show that log del…

We establish the optimal upper bounds for cone angles of K\"ahler-Einstein metrics with conical singularities along smooth anticanonical divisors on smooth K-unstable del Pezzo surfaces.

We prove the existence of singular del Pezzo surfaces that are neither K-semistable nor contain any anticanonical polar cylinder.

We classify toric log del Pezzo surfaces of Picard number one by introducing the notion, cascades. As an application, we show that if such a surface is K\"ahler-Einstein, then it should admit a special cascade, and it satisfies the equality…

Let k be an uncountable field of characteristic different from two. We show that a very general hypersurface of dimension N>2 and degree at least $\log_2N +2$ is not stably rational over the algebraic closure of k.

In this paper we obtain necessary and sufficient condition for existence of del Pezzo surfaces of degree $5$ and $6$ over a field $K$ with a prescribed action of absolute Galois group $\text{Gal} ( K^{\text{sep}}/K)$ on the graph of…

We study the arithmetic of del Pezzo surfaces $Y$ of degree 2 over a function field, and in particular, the cokernel of the homomorphism from the Picard group to the Galois-invariants of the geometric Picard group $\operatorname{Pic} Y…