On the second sectional geometric genus of quasi-polarized manifolds.
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 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 stability of the tangent bundle of Fano manifolds.
On the strange duality conjecture for abelian surfaces
We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of equal ranks and ber degree 1. The birational type of the moduli space of sheaves is also investigated. Generalizations to arbitrary product elliptic surfaces are given.
On the structure of linked 3-folds.
The structure of 3-folds in P6 which are generally linked via a complete intersection (f1,f2,f3) to 3-folds in P6 of degree d ≤ 5 is determined. We also give three new examples of smooth 3-folds in P6 of degree 11 and genus 9. These examples are obtained via liaison. The first two are 3-folds linked via a complete intersection (2,3,3) to 3-folds in P6 of degree 7: (i) the hyperquadric fibration over P1 and (ii) the scroll over P2. The third example is Pfaffian linked to a 3-dimensional quadric in...
On the Torelli problem for kählerian surfaces
On the uniqueness of elliptic K3 surfaces with maximal singular fibre
We explicitly determine the elliptic surfaces with section and maximal singular fibre. If the characteristic of the ground field is different from , for each of the two possible maximal fibre types, and , the surface is unique. In characteristic the maximal fibre types are and , and there exist two (resp. one) one-parameter families of such surfaces.
On the variational Torelli problem for complete intersections
On the zeta function of a hypersurface
On threefolds admitting a bielliptic curve as abstract complete intersection.
On total reality of meromorphic functions
We show that, if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points, then it is conjugate to a real meromorphic function by a suitable projective automorphism of the image.
On triple curves through a rational triple point of a surface
Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ and F has rational triple points. We classify the rational triple points through which such a curve C can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.
On two conjectures of Hartshorne's.
On Two Types of Surfaces of General Type with Vanishing Geometric Genus.
On unions of scrolls along linear spaces
On Unirationality of Supersingular Surfaces.
On unlikely intersections of complex varieties with tori