Related papers: Saturation of algebraic surfaces
Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…
We introduce extremal affine surface areas in a functional setting. We show their main properties. Among them are linear invariance, isoperimetric inequalities and monotonicity properties. We establish a new duality formula, which shows…
Surfaces of general type with canonical map of degree d bigger than 8 have bounded geometric genus and irregularity. In particular the irregularity is at most 2 if d>= 10. In the present paper, the existence of surfaces with d=10 and all…
We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a…
We investigate two notions of saturation for partial planar embeddings of maximal planar graphs. Let $G = (V, E) $ be a vertex-labeled maximal planar graph on $ n $ vertices, which by definition has $3n - 6$ edges. We say that a labeled…
Poonen and Gabber independently showed that any smooth geometrically irreducible projective scheme over a finite field has a smooth space filling curve, that is, a smooth curve defined over the field and passes through all points over the…
In previous works, G. Tomassini and the authors studied and classified complex surfaces admitting a real-analytic pluri-subharmonic exhaustion function; let $X$ be such a surface and $D\subseteq X$ a domain admitting a \emph{continuous}…
Given a smooth complex variety $X$, an algebraically skew embedding of $X$ is an embedding of $X$ into a complex projective space $\mathbb{P}^N$ such that for any two points $x,y\in X$, their embedded tangent spaces in $\mathbb{P}^N$ do not…
We give a novel and effective criterion for algebraicity of rational normal analytic surfaces constructed from resolving the singularity of an irreducible curve-germ on $CP^2$ and contracting the strict transform of a given line and all but…
Conserved charges in theories with gauge symmetries are supported on codimension-2 surfaces in the bulk spacetime. It has recently been suggested that various classical formulations of gravity dynamics display different symmetries, and…
For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative algebra by a version of the Hall…
Automated theorem provers (ATPs) can disprove conjectures by saturating a set of clauses, but the resulting saturated sets are opaque certificates. In the unit equational fragment, a saturated set can in fact be read as a convergent rewrite…
We introduce and study birational invariants for foliations on projective surfaces built from the adjoint linear series of positive powers of the canonical bundle of the foliation. We apply the results in order to investigate the effective…
The saturation number of a graph $G$ is the cardinality of any smallest maximal matching of $G$, and it is denoted by $s(G)$. Fullerene graphs are cubic planar graphs with exactly twelve 5-faces; all the other faces are hexagons. They are…
Translation surfaces can be defined in an elementary way via polygons, and arise naturally in in the study of various basic dynamical systems. They can also be defined as Abelian differentials on Riemann surfaces, and have moduli spaces…
Convex algebraic geometry concerns the interplay between optimization theory and real algebraic geometry. Its objects of study include convex semialgebraic sets that arise in semidefinite programming and from sums of squares. This article…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes…
This is a first graduate course in algebraic geometry. It aims to give the student a lift up into the subject at the research level, with lots of interesting topics taken from the classification of surfaces, and a human-oriented discussion…
We develop basic notions and methods of algebraic geometry over the algebraic objects called hyperrings. Roughly speaking, hyperrings generalize rings in such a way that an addition is `multi-valued'. This paper largely consisits of two…