Related papers: Classification of log Enriques surfaces with delta…
We calculate the dimension of the locus of elliptic surfaces over P^1 with a section and a given Picard number, in the corresponding moduli space.
We determine which connected surfaces can be partitioned into topological circles. There are exactly seven such surfaces up to homeomorphism: those of finite type, of Euler characteristic zero, and with compact boundary components. As a…
We give a proof of the Morrison-Kawamata cone conjecture for Enriques surfaces independent of their characteristic. It is based on the analysis of certain generically finite morphisms of degree two.
The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as $3$ classes: a sequence of two-parameter families of $2$-layer earth map tilings with $2n$ $(n\ge3)$ tiles, a one-parameter family of…
This is an exposition of the homological classification of actions of surface groups on the plane, in every degree of smoothness.
Rank-2 and rank-3 tensors are almost all identifiable with only few exceptions. We classify them all together with the dimensions and the structures of all the sets evincing the rank.
We derive simple formulas for the basic numerical invariants of a singular surface with Picard number one obtained by blowups and contractions of the four-line configuration in the plane. As an application, we establish the smallest…
We give a complete equisingular deformation classification of simple spatial quartic surfaces which are in fact $K3$-surfaces.
This paper is an announcement of the minimal model theory for log surfaces in all characteristics and contains some related results including a simplified proof of the Artin-Keel contraction theorem in the surface case.
A {\em $1-$vertex triangulation} of an oriented compact surface $S$ of genus $g$ is an embedded graph $T\subset S$ with a unique vertex such that all connected components of $S\setminus T$ are triangles (adjacent to exactly 3 edges of $T$).…
We give a classification and a construction of all smooth $(n-1)$-dimensional varieties of lines in ${\bf P}\sp n$ verifying that all their lines meet a curve. This also gives a complete classification of $(n-1)$-scrolls over a curve…
We perform the analytic classification of plane branches of multiplicity less or equal than four.
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…
We investigate the classification of topological quandles on some simple manifolds. Precisely we classify all Alexander quandle structures, up to isomorphism, on the real line and the unit circle. For the closed unit interval $[0, 1]$, we…
We consider two classes of non-toric log del Pezzo $\mathbb{C}^*$-surfaces: on the one side the 1/3-log canonical ones and on the other side those of Picard number one and Gorenstein index at most 65. In each of the two classes we figure…
Hypersurfaces of manifolds of constant nonzero sectional curvature are classificated according their restricted homogeneous holonomy groups.
We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model…
We give a complete classification of Q_l-cohomology projective planes with isolated ADE-singularities and numerically trivial canonical bundle in odd characteristic. This leads to a beautiful relation with certain Enriques surfaces which…
Let $(S,L)$ be a general polarized Enriques surface, with $L$ not numerically 2-divisible. We prove the existence of regular components of all Severi varieties of irreducible $\delta$-nodal curves in the linear system $|L|$, with $0\leq…
We establish regularity results for critical points to energies of immersed surfaces depending on the first and the second fundamental form exclusively. These results hold for a large class of intrinsic elliptic Lagrangians which are…