相关论文: Burniat surfaces III: deformations of automorphism…

We prove in one go that each of the 4 families of Burniat surfaces with K^2 = 6,5,4, is a connected component of the moduli space of surfaces of general type. We prove also the rationality of each component. In the nodal case (one of the…

This is the first part of a guide to deformations and moduli, especially viewed from the perspective of algebraic surfaces (the simplest higher dimensional varieties). It contains also new results, regarding the question of local…

The article is a slightly extended version of the talk, with the same title, which I gave at the Kinosaki Symposium on Algebraic Geometry in October 2011, and dealing with the classification of complex projective surfaces of general type…

Let S be a minimal surface of general type with $p_g(S)=0$ and such that the bicanonical map $\phi:S\to \pp^{K^2_S}$ is a morphism: then the degree of $\phi$ is at most 4 and if it is equal to 4 then $K^2_S\le 6$. Here we prove that if…

This is the first in a series of articles on the moduli spaces of Burniat surfaces. We prove that Burniat surfaces are Inoue surfaces and we calculate their fundamental groups. As a main result of this paper we prove that every smooth…

In this article we construct three new families of surfaces of general type with p_g = q = 0,K^2 = 6, and seven new families of surfaces of general type with p_g = q = 1, K^2 = 6, realizing 10 new fundamental groups. We also show that these…

In this paper, one of a series devoted to the classification, the moduli spaces and the discovery of new surfaces of general type with geometric genus p_g= 0, we generalize a classical construction method due to Burniat (and revisited by…

We describe explicitly the geometric KSBA compactifications, obtained by adding slc surfaces~$X$ with ample canonical class, of moduli spaces of Burniat surfaces of degrees $K^2=5$, $4$ and $3$.

We describe explicitly the geometric compactifications, obtained by adding slc surfaces $X$ with ample canonical class, for two connected components in the moduli space of surfaces of general type: Campedelli surfaces with $\pi_1(X)=\mathbb…

We describe compactifications of moduli spaces of Burniat surfaces with $2\leq K_{X}^{2}\leq5$ obtained by adding KSBA surfaces, i.e. slc surfaces $X$ with ample canonical class $K_{X}$.

We construct a 4-dimensional family of surfaces of general type with p_g=0 and K^2=3 and fundamental group Z/2xQ_8, where Q_8 is the quaternion group. The family constructed contains the Burniat surfaces with K^2=3. Additionally, we…

Let $S$ be a minimal surface of general type with $p_{g}(S)=0$ and $K^{2}_{S}=4$. Assume the bicanonical map $\varphi$ of $S$ is a morphism of degree $4$ such that the image of $\varphi$ is smooth. Then we prove that the surface $S$ is a…

We study the geometry and arithmetic of so-called primary Burniat surfaces, a family of surfaces of general type arising as smooth bidouble covers of a del Pezzo surface of degree 6 and at the same time as \'etale quotients of certain…

Surfaces of general type with geometric genus $p_g=0$, which can be given as Galois covering of the projective plane branched over an arrangement of lines with Galois group $G=(\mathbb Z/q\mathbb Z)^k$, where $k\geq 2$ and $q$ is a prime…

We classify minimal surfaces $S$ of general type with $p_g=q=2$ and $K_S^2=6$ whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth,…

This paper studies deformations and birational maps between singular moduli spaces of semistable sheaves with 2-divisible Mukai vectors on K3 surfaces. It is showed that under certain conditions, two such moduli spaces of the same dimension…

This paper is dedicated to the study of deformations of coassociative 4-folds in a G_2 manifold which have conical singularities. We stratify the types of deformations allowed into three problems. The main result for each problem states…

In this short note, we extend the results of [Alexeev-Orlov, 2012] about Picard groups of Burniat surfaces with $K^2=6$ to the cases of $2\le K^2\le 5$. We also compute the semigroup of effective divisors on Burniat surfaces with $K^2=6$.…

We give infinite series of groups Gamma and of compact complex surfaces of general type S with fundamental group Gamma such that 1) Any surface S' with the same Euler number as S, and fundamental group Gamma, is diffeomorphic to S. 2) The…

The purpose of this article is to study the deformations of smooth surfaces $X$ of general type whose canonical map is a finite, degree 2 morphism onto a minimal rational surface or onto $\mathbf F_1$, embedded in projective space by a very…