Related papers: Endomorphisms of the plane preserving a pencil of …
We characterise, in terms of Dixmier-Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determining the stable reduction types of non-hyperelliptic curves of…
This note is an attempt to relate explicitly the geometric and algebraic properties of a space curve that is contained in some double plane. We show in particular that the minimal generators of the homogeneous ideal of such a curve can be…
We give complete geometric invariants of cobordisms of fold maps with oriented singular set and cobordisms of even codimensional fold maps. These invariants are given in terms of cobordisms of stably framed manifolds and cobordisms of…
Consider the collection of edge bicolorings of a graph that is cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colorings under two relations: reversing colors around a face and…
We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts and compute the total number of curves counted with…
Let $G$ be a subgroup of the three dimensional projective group $\mathrm{PGL}(3,q)$ defined over a finite field $\mathbb{F}_q$ of order $q$, viewed as a subgroup of $\mathrm{PGL}(3,K)$ where $K$ is an algebraic closure of $\mathbb{F}_q$.…
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.
The present paper deals with a study of curves on a smooth surface whose position vector always lies in the tangent plane of the surface and it is proved that such curves remain invariant under isometry of surfaces. It is also shown that…
We determine endomorphism algebras of abelian surfaces with quaternion multiplication.
Abstractly, tropical hyperelliptic curves are metric graphs that admit a two-to-one harmonic morphism to a tree. They also appear as embedded tropical curves in the plane arising from triangulations of polygons with all interior lattice…
In this paper we extend the properties of ordinary points of curves [10] to ordinary closed points of one-dimensional affine reduced schemes and then to ordinary subvarieties of codimension one.
We determine obstructedness or unobstructedness of (holomorphic) Poisson deformations of ruled surfaces over an elliptic curve.
We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
A self-avoiding plane-filling curve cannot be periodic, but we show that it can satisfy the local isomorphism property. We investigate three families of coverings of the plane by finite sets of nonoverlapping self-avoiding curves which…
These results complete our paper in Hiroshima Mathematical Journal, vol. 42, pp. 37-75. Let C be a covering of the plane by disjoint complete folding curves which satisfies the local isomorphism property. We show that C is locally…
We characterize all groups which can occur as the topological symmetry group or the orientation preserving topological symmetry group of some embedding of the Petersen graph in S^3.
We give examples of endperiodic automorphisms.
We bound the genus of a projective curve lying on a complete intersection surface in terms of its degree and the degrees of the defining equations of the surface on which it lies.
We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.
We consider a method of construction of self-similar dendrites on a plane and establish main topological and metric properties of resulting class of dendrites.