Related papers: Gorenstein stable Godeaux surfaces
We study quotients of mapping class groups (\Gamma_{g,1}) of oriented surfaces with one boundary component by terms of their Johnson filtrations, and we show that the homology of these quotients with suitable systems of twisted coefficients…
We study slope stability of smooth surfaces and its connection with exceptional divisors. We show that a surface containing an exceptional divisor with arithmetic genus at least two is slope unstable for some polarisation. In the converse…
Koszulness of Gorenstein quadratic algebras of small socle degree is studied. In this note, we construct non-Koszul Gorenstein quadratic toric ring such that its socle degree is more than 3 by using stable set polytopes.
We study stable rationality properties of conic bundles over rational surfaces.
We introduce the class of weakly log canonical singularities, a natural generalization of semi-log canonical singularities. Toric varieties (associated to toric face rings, possibly non-normal or reducible) which have weakly (semi-) log…
If a smooth, geometrically rational surface over a finite field is not rational over that field, then over some finite extension of that field the Brauer group of the surface is nonzero. In particular such a surface is not stably rational.…
We prove the regularity conjecture, namely Eisenbud-Goto conjecture, for a normal surface with rational, Gorenstein elliptic and log canonical singularities. Along the way, we bound the regularity for a dimension zero scheme by its Loewy…
We discuss the relationship between the trace ideal of the canonical module and pseudo-Gorensteinness. In particular, under certain mild assumptions, we show that every pseudo-Gorenstein nearly Gorenstein graded domain is Gorenstein. As an…
We study focal surfaces of (wave) fronts associated to unbounded principal curvatures near non-degenerate singular points of initial fronts. We give characterizations of singularities of those focal surfaces in terms of types of…
In this paper the detailed classification of three-dimensional exceptional canonical hypersurface singularities which don't satisfy the condition of well-formedness is given. This result completes the classification of three-dimensional…
In this article we classify quadruple Galois canonical covers of smooth surfaces of minimal degree. The classification shows that they are either non-simple cyclic covers or bi-double covers. If they are bi-double then they are all fiber…
We show that a properly stratified algebra is Gorenstein if and only if the characteristic tilting module coincides with the characteristic cotilting module. We further show that properly stratified Gorenstein algebras $A$ enjoy strong…
Let $X$ be a normal arithmetically Gorenstein scheme in ${\mathbb P}^n$. We give a criterion for all codimension two ACM subschemes of $X$ to be in the same Gorenstein biliaison class on $X$, in terms of the category of ACM sheaves on $X$.…
We classify and study trigonal curves in Hirzebruch surfaces admitting dihedral Galois coverings. As a consequence, we obtain certain restrictions on the fundamental group of a plane curve~$D$ with a singular point of multiplicity $(\deg…
The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…
We give a new criterion for when a resolution of a surface of general type with canonical singularities has big cotangent bundle and a new lower bound for the values of $d$ for which there is a surface with big cotangent bundle that is…
We construct examples of algebraic surfaces with interesting fundamental groups.
We give examples of K-unstable singular del Pezzo surfaces which are weighted hypersurfaces with index 2.
In this paper we propose an approach to investigate the canonical rings of surfaces of general type whose canonical system has isolated base points and yields a birational map onto its image. We apply then the method in the concrete case of…
This is the final paper in a series of four, concerning the surface $T \times T$ embedded in $\mathbb{CP}^8$, where $T$ is a the one dimensional torus. In this paper we compute the fundamental group of the Galois cover of the surface with…