Related papers: Computing invariants of semi-log-canonical surface…

In this note, we prove a 2-systolic inequality on compact positive scalar curvature K\"ahler surfaces admitting a nonconstant holomorphic map to a positive-genus compact Riemann surface. According to the classification of positive scalar…

Minimal algebraic surfaces of general type with the smallest possible invariants have geometric genus zero and K^2=1 and are usually called "numerical Godeaux surfaces". Although they have been studied by several authors, their complete…

Among log canonical surface singularities, the ones which have a rational homology disk smoothing are the cyclic quotient singularities $\frac{1}{n^2}(1,na-1)$ with gcd$(a,n)=1$, and three distinguished elliptic quotient singularities. We…

In this paper we construct a new family of simply connected minimal complex surfaces of general type with $p_g=1$, $q=0$, and $K^2=3, 4, 5, 6, 8$ using a $\mathbb{Q}$-Gorenstein smoothing theory. We also reconstruct minimal complex surfaces…

Let X be a K3 surface with an involution g which has non-empty fixed locus X^g and acts non-trivially on a non-zero holomorphic 2-form. We shall construct all such pairs (X, g) in a canonical way, from some better known double coverings of…

In this paper we collect some results on the obstruction spaces for rational surface singularities and minimally elliptic surface singularities. Based on the known results we calculate higher obstruction spaces for such surface…

Canonical principal parameters are introduced for surfaces in $\mathbb R^3$ without umbilical points. It is proved that in these parameters the surface is determined (up to position in space) by a pair of invariants satisfying a partial…

This paper numerically computes the topological and smooth invariants of Eschenburg spaces with small fourth cohomology group, following Kruggel's determination of the Kreck-Stolz invariants of Eschenburg spaces that satisfy condition C.…

In this paper we characterize two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic from the viewpoint of the initial term of the defining equation. As an application, we prove a conjecture about a uniform bound of…

A surface with an involution can be viewed as a $C_2$-space where $C_2$ is the cyclic group of order two. Using the classification of $C_2$-surfaces given by Dugger, we compute the $RO(C_2)$-graded Bredon cohomology of all $C_2$-surfaces in…

We give algorithms of computing bases of logarithmic cohomology groups for square-free polynomials in two variables. (Fixed typos of v1)

Let $X$ be surface with isolated singularities in the complex projective space $P^3$ and let denote $Y$ the smooth part of $X$. In this note we discuss some aspects of the topology of such quasi-projective surfaces $Y$: the fundamental…

We construct a normal projective $\mathbb{Q}$-Gorenstein surface over an algebraically closed field whose canonical ring is not finitely generated. Moreover, we provide a counterexample to the minimal model program for…

We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free countably compact topological inverse semigroups.

Smooth surfaces have finitely generated canonical rings and projective canonical models. For normal surfaces, however, the graded ring of multicanonical sections is possibly nonnoetherian, such that the corresponding homogeneous spectrum is…

We give a survey of our previous work on relatively minimal isotrivial fibrations $\alpha \colon X \to C$, where $X$ is a smooth, projective surface and $C$ is a curve. In particular, we consider two inequalities involving the numerical…

We first describe the numerical invariants attached to the second fundamental form of a spacelike surface in four-dimensional Minkowski space. We then study the configuration of the nu-principal curvature lines on a spacelike surface, when…

We consider the deformation spaces of some singular product-quotient surfaces $X=(C_1 \times C_2)/G$, where the curves $C_i$ have genus 3 and the group $G$ is isomorphic to $\mathbb{Z}_4$. As a by-product, we give a new construction of…

In this paper we characterize logarithmic surfaces which admit K\"ahler-Einstein metrics with negative scalar curvature and small edge singularities along a normal crossing divisor.

We give an existence result on (H,A)-stable sheaves on a K3 or abelian surface X with primitive triple of invariants (rank,first Chern class,Euler characteristics) in the integral cohomology lattice. Such a result yields the existence of…