We reprove some results about affine complete intersections.

In this survey we present recent results in the study of the medial axes of sets definable in polynomially bounded o-minimal structures. We take the novel point of view of singularity theory. Indeed, it has been observed ...

We study negative curves on surfaces obtained by blowing up special configurations of points in P2. Our main results concern the following configurations: very general points on a cubic, 3–torsion points on an elliptic ...

The containment problem between symbolic and ordinary powers of homogeneous ideals has stimulated a lot of interesting research recently. In the most basic case of points in P2 and powers I(3) and I2, there is a number of ...

In the present note we investigate to which extent the configuration of 9 lines intersecting in triples in 12 points is determined by these incidences. We show that up to a projective automorphism there is exactly one such ...

We present a survey of the research on rings of polynomial constants and fields of rational constants of cyclic factorizable derivations in polynomial rings over fields of characteristic zero.

We investigate properties of the contact exponent (in the sense of Hironaka [Hi]) of plane algebroid curve singularities over algebraically closed fields of arbitrary characteristic. We prove that the contact exponent is ...

Points and lines can be regarded as the simplest geometrical objects. Incidence relations between them have been studied since ancient times. Strangely enough our knowledge of this area of mathematics is still far from ...

In this article all rings and algebras are commutative with identity, and we denote by R[x] the ring of polynomials over a ring R in one variable x. We describe rings R such that all subalgebras of R[x] are finitely generated ...