Related papers: Ordinary Subvarieties of codimension one

A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

We give some results on quadratic normality of reducible curves canonically embedded and partially extend this study to their projective normality.

We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteration of the map, while the whole subvariety is not. Several…

In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we…

The main purpose of this paper is to show that ideas of deformation theory can be applied to "infinite dimensional geometry". We develop the deformation theory of Brody curves. Brody curve is a kind of holomorphic map from the complex plane…

We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.

These lectures give a short introduction to the study of curves on algebraic varieties. After an elementary proof of the dimension formula for the space of curves, we summarize the basic properties of uniruled and of rationally connected…

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…

We consider semi-orthogonal decompositions of derived categories for 3-dimensional projective varieties in the case when the varieties have ordinary double points.

This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…

In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.

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…

Let $Z$ be a projective hypersurface such that its underlying reduced variety has only isolated singularities. In case its irreducible components have constant multiplicities, for instance if $\dim Z>1$, we show that the spectrum of its…

Here we introduce the concept of special effect curve which permits to study, from a different point of view, special linear systems in P^2, i.e. linear system with general multiple base points whose effective dimension is strictly greater…

Let $N$ be a point of an orbit closure $\bar{O_M}$ in a module variety such that its orbit $O_N$ has codimension two in $\bar{O_M}$. We show that under some additional conditions the pointed variety $(\bar{O_M},N)$ is smoothly equivalent to…

The main purpose of this paper is twofold. We first want to analyze in details the meaningful geometric aspect of the method introduced in the previous paper [12], concerning regularity of families of irreducible, nodal "curves" on a…

We classify the subvarieties of infinite dimensional affine space that are stable under the infinite symmetric group. We determine the defining equations and point sets of these varieties as well as the containments between them.

Let M and N be two representations of an extended Dynkin quiver such that the orbit O_N of N is contained in the orbit closure \bar{O_M} and has codimension two. We show that the pointed variety $(\bar{O_M},N)$ is smoothly equivalent to a…

In this article a complete set of invariants for ordinary quartic curves in characteristic 2 is computed.