Related papers: KSBA surfaces with elliptic quotient singularities…

Algebraically simply connected surfaces of general type with p_g=q=0 and 1\le K^2\le 4 in positive characteristic (with one exception in K^2=4) are presented by using a Q-Gorenstein smoothing of two-dimensional toric singularities, a…

Let $C$ be a smooth projective curve defined over $\Qbar$, let $\pi:\mathcal{E}\lra C$ be an elliptic surface and let $\sigma_{P_1},\sigma_{P_2},\sigma_{Q}$ be sections of $\pi$ (corresponding to points $P_1,P_2, Q$ of the generic fiber $E$…

We apply the complex analysis over the double numbers $D$ to study the minimal time-like surfaces in $R^4_2$. A minimal time-like surface which is free of degenerate points is said to be of general type. We divide the minimal time-like…

This article consists of two parts. The first part is a survey on the normal reduction numbers of normal surface singularities. It includes results on elliptic singularities, cone-like singularities and homogeneous hypersurface…

By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be…

We use classification of non-symplectic automorphisms of K3 surfaces to obtain a partial classification of log del Pezzo surfaces of index three. We can classify those with "Multiple Smooth Divisor Property", whose definition we will give.…

We prove that the affine cone over a general primitively polarised K3 surface of genus g is smoothable if and only if g\le 10 or g=12. We also give several examples of singularities with special behaviour, such as surfaces whose affine cone…

Minimal irregular surfaces of general type satisfy K^2\geq 2p_g. In this paper we classify those surfaces for which the equality K^2=2p_g holds.

We compute equations for Coughlan's family of Godeaux surfaces with torsion $\mathbb Z/2$, which we call $\mathbb Z/2$-Godeaux surfaces, and we show that it is (at most) 7 dimensional. We classify non-rational KSBA degenerations $W$ of…

We construct three sequences of regular surfaces of general type with unbounded numerical invariants whose canonical map is 2-to-1 onto a canonically embedded surface. Only sporadic examples of surfaces with these properties were previously…

We introduce an inseparable version of Kummer surfaces. It is defined as a supersingular K3 surface in characteristic 2 with 16 smooth rational curves forming a certain configuration and satisfying a suitable divisibility condition. The…

Esnault-Viehweg developed the theory of cyclic branched coverings $\tilde X\to X$ of smooth surfaces providing a very explicit formula for the decomposition of $H^1(\tilde X,\mathbb{C})$ in terms of a resolution of the ramification locus.…

The aim of the paper is to provide a series of new examples of smooth surfaces in P^4, not of general type, in degrees varying from 12 up to 14, and to describe their geometry. By using mainly syzygies and liaison techniques, we construct…

In this note, we construct a minimal surface of general type with geometric genus p g = 4, self-intersection of the canonical divisor K^2 = 32 and irregularity q = 1 such that its canonical map is an abelian cover of degree 16 of P^1 x P^1.

We study the moduli space of minimal surfaces of general type with $K_S^2 = 1$ and $p_g = 2$ and show that it is irreducible, has dimension $28$ and admits a compactification which is unirational.

We study the relation between birational singularities of 1-foliations and those of their quotients. We prove that the quotient $X/\mathcal{F}$ is log canonical (resp. klt) if and only if $\mathcal{F}$ is $\frac{p-1}{p}$-log canonical…

According to a well-known theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity. At the opposite extremity…

Let $X$ be a surface of general type with maximal Albanese dimension over an algebraically closed field of characteristic greater than two: we prove that if $K_X^2<\frac{9}{2}\chi(\mathcal{O}_X)$, one has $K_X^2\geq…

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient…

In this paper we construct a simply connected, minimal, complex surface of general type with p_g=0 and K^2=2 using a rational blow-down surgery and Q-Gorenstein smoothing theory.