On the Severi problem.
On the S-fundamental group scheme
We introduce a new fundamental group scheme for varieties defined over an algebraically closed (or just perfect) field of positive characteristic and we use it to study generalization of C. Simpson’s results to positive characteristic. We also study the properties of this group and we prove Lefschetz type theorems.
On the Shafarevich and Tate conjectures for hyperkähler varieties.
On the Shafarevich-Tate group of the jacobian of a quotient of the Fermat curvature.
On the Shintani zeta function for the space of binary quadratic forms.
On the Siegel modular function field of degree three
On the singularities of Polar curves.
On the Singularities of Weakly Normal Varieties.
On the smallest degree of a surface containing a space curve
Sia una curva dello spazio di grado contenuta in una superficie di grado e non in una di grado . Se è integra, allora ; questo limite superiore, raggiunto in alcuni casi (cfr. [5]), non vale però per curve arbitrarie (cfr. [?, 3 (iii)]). Ogni curva dello spazio (anche non ridotta o riducibile) può essere ottenuta come schema degli zero di una sezione non nulla di un opportuno fascio riflessivo di rango 2. Mediante i fasci riflessivi, siamo in grado di estendere alle curve riducibili...
On the Smoothing and Deformation of Perfect Varieties.
On the solutions of certain diagonal quadratic equations and Lang's conjecture
On the space curves with the same dual varietey.
On the space curves with the same image under the Gauss maps.
On the space of morphisms into generic real algebraic varieties
We introduce a notion of generic real algebraic variety and we study the space of morphisms into these varieties. Let be a real algebraic variety. We say that is generic if there exist a finite family of irreducible real algebraic curves with genus and a biregular embedding of into the product variety . A bijective map from a real algebraic variety to is called weak change of the algebraic structure of if it is regular and its inverse is a Nash map. Generic real algebraic varieties...
On the space of real algebraic morphisms
In this Note, we announce several results concerning basic properties of the spaces of morphisms between real algebraic varieties. Our results show a surprising intrinsic rigidity of Real Algebraic Geometry and illustrate the great distance which, in some sense, exists between this geometry and Real Nash one. Let us give an example of this rigidity. An affine real algebraic variety is rigid if, for each affine irreducible real algebraic variety , the set of all nonconstant regular morphisms from...
On the space of Shottky-Mumford curves
On the span invariant for cubic similarity
Given a real n×n matrix A, we make some conjectures and prove partial results about the range of the function that maps the n-tuple x into the entrywise kth power of the n-tuple Ax. This is of interest in the study of the Jacobian Conjecture.
On the Spannedness and Very Ampleness of Certain Line Bundles on the Blow-ups of IP2C and Fr .
On the spannedness of adjunction of vector bundles.
On the spectral geometry of algebraic curves.