Nodal surfaces with obstructed deformations

In this text we show that the deformation space of a nodal surface X of degree d is smooth and of the expected dimension if \(d\le 7\) or \(d\ge 8\) and X has at most \(4d-5\) nodes (The case \(d\le 7\) was previously covered by Alexandru Dimca using different techniques). For \(d\ge 8\) we give explicit examples of nodal surfaces with \(4d-4\) nodes, for which the tangent space to the deformation space has larger dimension than expected.     

Some smooth Finsler deformations of hyperbolic surfaces

Given a closed hyperbolic Riemannian surface, the aim of the present paper is to describe an explicit construction of smooth deformations of the hyperbolic metric into Finsler metrics that are not Riemannian and whose properties are such that the classical Riemannian results about entropy rigidity, marked length spectrum rigidity and boundary rigidity all fail to extend to the Finsler category.     

Isometric deformations of surfaces preserving the third fundamental form

We study the following problem: To what extend is a surface in the Euclidean space \(\mathbb{R}^{4}\) determined by the third fundamental form? We prove the existence of families of surfaces in \(\mathbb{R}^{4}\) which allow isometric deformations with isometric but not congruent Gaussian images. In particular, we provide a method which gives locally all surfaces in \(\mathbb{ R}^{4}\) with conformal Gauss map that allow such deformations. As a consequence, we have a way for constructing non-spherical pseudoumbilical surfaces in \(\mathbb{R}^{4}.\)     

Normal and tangential geodesic deformations of the surfaces of revolution

We study special infinitesimal geodesic deformations of the surfaces of revolution in the Euclidean space E ³.     

Algebraic deformations of compact Kähler surfaces

A short proof is given of Kodaira's result that every compact kähler surface is a deformation of an algebraic surface under the extra assumption that all infinitesimal deformations are unobstructed.     

Flat grafting deformations of quadratic differentials on surfaces

Geometriae Dedicata - In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces....     

Seshadri constants in a family of surfaces

The aim of this note is to study local and global Seshadri constants for a family of smooth surfaces with prescribed polarization. Received: 16 April 2001 / Published online: 26 April 2002     

Algebraic deformations of compact Kähler surfaces II

In the first version of this paper, a short proof was given of Kodaira’s result that every compact Kähler surface is a deformation of an algebraic surface under the extra assumption that the infinitesimal deformations of the surface were unobstructed. In this paper, the extra assumption is removed.