Related papers: Topology of plane algebraic curves: the algebraic …
We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose…
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.
We study the existence of some irreducible projective plane curves of degree~$8$ with some prescribed topological type of singularities in the algebraic and symplectic worlds.
We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
We give an overview of various recent results concerning the topology of symplectic 4-manifolds and singular plane curves, using branched covers and isotopy problems as a unifying theme. While this paper does not contain any new results, we…
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…
We present a complete classification of complex plane algebraic curves, equipped with the induced Euclidean, up to global bilipschitz homeomorphism.
We study the structure of collections of algebraic curves in three dimensions that have many curve-curve incidences. In particular, let $k$ be a field and let $\mathcal{L}$ be a collection of $n$ space curves in $k^3$, with…
We study the notion of geometric structures for toposes: This generalizes the notion of (X,G) manifolds. We give some applications to algebraic geometry
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
We study topological properties of the graph topology.
We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.
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…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
In this paper we prove the topological uniqueness of maximal arrangements of a real plane algebraic curve with respect to three lines. More generally, we prove the topological uniqueness of a maximally arranged algebraic curve on a real…
We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an…
In this present paper, we study the splitting of nodal plane curves with respect to contact conics. We define the notion of splitting type of such curves and show that it can be used as an invariant to distinguish the embedded topology of…