On projective varieties of minimal degree.
On proximity relations for valuations dominating a two-dimensional regular local ring.
The purpose of this paper is to define a new numerical invariant of valuations centered in a regular two-dimensional regular local ring. For this, we define a sequence of non-negative rational numbers δν = {δν(j)}j ≥ 0 which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation ν. This sequence is characterized by seven combinatorial properties, so that any sequence of non-negative rational numbers having the above properties...
On Quadratic forms isotropic over the function field of a comic.
On quadrirational Yang-Baxter maps.
On ramification and genus of recursive towers.
On ramified covers of the projective plane II: Generalizing Segre’s theory
The classical Segre theory gives a necessary and sufficient condition for a plane curve to be a branch curve of a (generic) projection of a smooth surface in . We generalize this result for smooth surfaces in a projective space of any dimension in the following way: given two plane curves, and , we give a necessary and sufficient condition for to be the branch curve of a surface in and to be the image of the double curve of a -model of . In the classical Segre theory, a plane curve...
On rank semistable vector bundles over an irreducible nodal curve of genus
Sia una curva irriducibile nodale di genere aritmetico . In queste note vogliamo mostrare come il sistema lineare delle quadriche, contenenti un opportuno modello proiettivo della curva, permette di descrivere i fibrati vettoriali semistabili, di rango , su .
On ranks of Jacobian varieties in prime degree extensions
T. Dokchitser [Acta Arith. 126 (2007)] showed that given an elliptic curve E defined over a number field K then there are infinitely many degree 3 extensions L/K for which the rank of E(L) is larger than E(K). In the present paper we show that the same is true if we replace 3 by any prime number. This result follows from a more general result establishing a similar property for the Jacobian varieties associated with curves defined by an equation of the shape f(y) = g(x) where f and g are polynomials...
On Rao's theorems and the Lazarsfeld-Rao property
On reconstruction of polynomial automorphisms
We extend results on reconstructing a polynomial automorphism from its restriction to the coordinate hyperplanes to some wider class of algebraic surfaces. We show that the algorithm proposed by M. Kwieciński in [K2] and based on Gröbner bases works also for this class of surfaces.
On ruled fields
Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.
On secant spaces to projective curves
On set theoretic complete intersections in IP3.
On set theoretic complete intersections in IP3 (Erratum).
On set theoretic complete intersections in P3k.
On singular moduli.
On Singularities of the Curves Belonging to some linear system in P2.
On smooth curves passing through rational surface singularities.
On Smoothable Curve Singularities: Local Methods.
On some algebraic and geometric extension of the theory of adjoints