相关论文: Unprojection and deformations of tertiary Burniat …

We continue our investigation of the connected components of the moduli space of surfaces of general type containing the Burniat surfaces, correcting a mistake in part II. We define the family of extended Burniat surfaces with K_S^2 = 4,…

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…

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…

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 study the extension of a hyperelliptic K3 surface to a Fano 6-fold. This determines a family of surfaces of general type with p_g=1, K^2=2 and hyperelliptic canonical curve, where each surface is a weighted complete intersection inside a…

In this article we exhibit certain projective degenerations of smooth $K3$ surfaces of degree $2g-2$ in $\Bbb P^g$ (whose Picard group is generated by the hyperplane class), to a union of two rational normal scrolls, and also to a union of…

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…

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of…

We construct a family of Fano fourfolds with the derived category of coherent sheaves of a general Enriques surface as semiorthogonal component. This improves a result of Kuznetsov, lowering the Fano dimension of a general Enriques surface…

We study Q-factorial terminal Fano 3-folds whose equations are modelled on those of the Segre embedding of P^2 x P^2. These lie in codimension 4 in their total anticanonical embedding and have Picard rank 2. They fit into the current state…

We discover a simple construction of a four-dimensional family of smooth surfaces of general type with $p_g(S)=q(S)=0$, $K^2_S=3$ with cyclic fundamental group $C_{14}$. We use a degeneration of the surfaces in this family to find…

It is shown that a smooth global deformation of quartic double solids, i.e. double covers of $\mathbb P^3$ branched along smooth quartics, is again a quartic double solid without assuming the projectivity of the global deformation. The…

We construct examples of surfaces of general type with $p_g=1$, $q=0$ and $K^2=6$. We use as key varieties Fano fourfolds and Calabi-Yau threefolds that are zero section of some special homogeneous vector bundle on Grassmannians. We link as…

We study threefolds of general type constructed as $\mathbb{Z}_2^s$-covers of weighted projective spaces with a particular focus on their invariants, deformation theory, and the behavior of the $m$-canonical map. For the invariants, we…

We give an explicit construction for the extension of a symmetric determinantal quartic K3 surface to a Fano 6-fold. Remarkably, the moduli of the 6-fold extension are in one-to-one correspondence with the moduli of the quartic surface. As…

Iterating the procedure of making a double cover over a given variety, we construct large families of smooth higher-dimensional Fano varieties of index 1. These varieties can be realized as complete intersections in various weighted…

We study Fano fourfolds of K3 type with a conic bundle structure. We construct direct geometrical links between these fourfolds and hyperK\"ahler varieties. As a result we describe families of nodal surfaces that can be seen as…

Motivated by the theory of Inoue-type varieties, we give a structure theorem for projective manifolds $W_0$ with the property of admitting a 1-parameter deformation where $W_t$ is a hypersurface in a projective smooth manifold $Z_t$. Their…

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 discover a family of surfaces of general type with $K^2=3$ and $p=q=0$ as free $C_{13}$ quotients of special linear cuts of the octonionic projective plane $\mathbb O \mathbb P^2$. A special member of the family has $3$ singularities of…