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

Hypersurfaces of manifolds of constant nonzero sectional curvature are classificated according their restricted homogeneous holonomy groups.

We complete the classification of automorphism groups of del Pezzo surfaces over algebraically closed fields of odd positive characteristic.

We show that a complete, two-sided, stable minimal hypersurface in $\mathbf{R}^5$ is flat.

In this paper we construct a full exceptional collection of sheaves on some family of log Del Pezzo surfaces, viewed as a smooth stack. These surfaces can be embedded as a quasi-smooth hypersurfaces into a certain weighted projective space,…

Let $S$ be a del Pezzo surface with at worst Du Val singularities of degree $2$ such that $S$ admits an $(-K_S)$-polar cylinder. In this article, we construct an $H$-polar cylinder for any ample $\mathbb{Q}$-divisor $H$ on $S$.

We classify log-canonical pairs $(X, \Delta)$ of dimension two with $K_X+\Delta$ an ample Cartier divisor with $(K_X+\Delta)^2=1$, giving some applications to stable surfaces with $K^2=1$. A rough classification is also given in the case…

Following Skorobogatov and Serganova we construct the embeddings of universal torsors over del Pezzo surfaces in the cones over flag varieties, considered as the closed orbits in the projectivization of quasiminiscule representations. We…

We classify isoparametric hypersurfaces in complex hyperbolic spaces.

In this paper, we found non-symplectic index of all supersingular K3 surfaces defined over a field of characteristic p>3.

This paper concerns some stability properties of higher dimensional catenoids in $\rr^{n+1}$ with $n\ge 3$. We prove that higher dimensional catenoids have index one. We use $\delta$-stablity for minimal hypersurfaces and show that the…

We study the space of smooth marked hypersurfaces in a given linear system. Specifically, we prove a homology h-principle to compare it with a space of sections of an appropriate jet bundle. Using rational models, we compute its rational…

We prove K-stability of smooth Fano 3-folds of Picard rank 3 and degree 20 that satisfy very explicit generality condition.

In this paper we study the problem of classifying pencils of curves of degree $d$ in $\mathbb{P}^2$ using geometric invariant theory. We consider the action of $SL(3)$ and we relate the stability of a pencil to the stability of its…

Stability version of the Prekopa-Leindler inequality for log-concave functions on the n-dimensional Euclidean space is established.

We announce a classification of genus 2 Veech surfaces in the stratum with a single double zero. Furthermore, we classify all completely periodic translation surfaces in genus 2.

We give new proofs of the K-polystability of two smooth Fano threefolds. One of them is a~smooth divisor in $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^2$ of degree $(1,1,1)$, which is unique up to isomorphism. Another one is the~blow…

We prove that a del Pezzo surface with Picard number one has at most four singular points.

In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type…

Let $K$ be a number field and $S$ a finite set of primes of $K$. Scholl proved that there are only finitely many $K$-isomorphism classes of del Pezzo surfaces of any degree $1 \le d \le 9$ over $K$ with good reduction away from $S$. Let…

We construct jacobians of plane quartics without complex multiplication, using Del Pezzo surfaces of degree 2.