Related papers: Some singular curves and surfaces arising from inv…
We give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs satisfying these properties. In…
In projectivized strata of meromorphic $1$-forms on elliptic curves with only one zero, the locus of residueless differentials is a complex curve endowed with a canonical complex projective structure. Drawing on the multi-scale…
We present a framework for constructing examples of smooth projective curves over number fields with explicitly given elements in their second K-group using elementary algebraic geometry. This leads to new examples for hyperelliptic curves…
A family of algebraic surfaces with many nondegenerate real singularities is introduced with the help of a construction, which has been used in previous works for the generation of substitution tilings.
We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.
For isolated complex hypersurface singularities with real defining equation we show the existence of a monodromy vector field such that complex conjugation intertwines the local monodromy diffeomorphism with its inverse. In particular, it…
For any positive integer $r$, we construct a smooth complex projective rational surface which has at least $r$ real forms not isomorphic over $\mathbb{R}$.
We examine the extent to which a smooth minimal complex projective surface X is determined by its derived category of coherent sheaves D(X). To do this we find, for each such surface X, the set of surfaces Y for which there exists a…
We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…
An expository description of smooth cubic curves in the real or complex projective plane.
We show that the isolated invariant branches globalize to algebraic curves, when we consider weak toric type complex hyperbolic foliations on projective toric ambient surfaces. To do it, we pass through a characterization of weak toric type…
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
In this paper, we prove some fundamental theorems for holomorphic curves on angular domain intersecting a hypersurface, finite set of fixed hyperplanes in general position and finite set of fixed hypersurfaces in general position on complex…
We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…
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…
This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.
Primitive points on the tower of modular curves $X_1(n)$ provide a finite "certificate set" for detecting isolated points above a fixed $j$-invariant: for a non-CM elliptic curve $E/\mathbb{Q}$, $j(E)$ arises from an isolated point on some…
We define a topological invariant of complex projective plane curves. As an application, we present new examples of arithmetic Zariski pairs.
A directed curve is a possibly singular curve with well-defined tangent lines along the curve. Then the tangent surface to a directed curve is naturally defined as the ruled surface by tangent geodesics to the curve, whenever any affine…
We study the relationship between singularities of finite-dimensional integrable systems and singularities of the corresponding spectral curves. For the large class of integrable systems on matrix polynomials, which is a general framework…