On the non-defectivity of non weak-defectivity of Segre-Veronese embeddings of products of projective spaces.
On the number of connected components of real abelian varieties that admit sufficiently many compley multiplications.
On the number of singular ponts of a real projective hypersurface.
On the osculatory behaviour of higher dimensional projective varieties.
We explore the geometry of the osculating spaces to projective verieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the existence of inflectionary points.
On the projective normality of complete linear series on an algebraic curve.
On the projective normality of the adjunction bundles.
On the projectivity of the moduli spaces of curves.
On the quantum cohomology of the plane, old and new, and a K3 analogue.
On the real X -ranks of points of P n (R) with respect to a real variety X ⊂ P n
Let X ⊂ Pn be an integral and non-degenerate m-dimensional variety defined over R. For any P ∈ Pn(R) the real X-rank r x,R(P) is the minimal cardinality of S ⊂ X(R) such that P ∈ . Here we extend to the real case an upper bound for the X-rank due to Landsberg and Teitler.
On the secant varieties to the osculating variety of a Veronese surface
In this paper we study the k-th osculating variety of the order d Veronese embedding of P n. In particular, for k=n=2 we show that the corresponding secant varieties have the expected dimension except in one case.
On the second sectional geometric genus of quasi-polarized manifolds.
On the Severi problem.
On the space curves with the same dual varietey.
On the stability of the restricted bundle of space curves contained in a quartic surface.
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 superadditivity of secant defects
On the tacnodes of configurations of conics in the projective plane.
On the theorem of de Franchis
On the weak non-defectivity of veronese embeddings of projective spaces
Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<(nn+x). Here we prove that the order x Veronese embedding ofP n is not weakly (k−1)-defective, i.e. for a general S⊃P n such that #(S) = k+1 the projective space | I 2S (x)| of all degree t hypersurfaces ofP n singular at each point of S has dimension (n/n+x )−1− k(n+1) (proved by Alexander and Hirschowitz) and a general F∈| I 2S (x)| has an ordinary double point at each P∈ S and Sing (F)=S.
On Thom Polynomials for A4(−) via Schur Functions
2000 Mathematics Subject Classification: 05E05, 14N10, 57R45.We study the structure of the Thom polynomials for A4(−) singularities. We analyze the Schur function expansions of these polynomials. We show that partitions indexing the Schur function expansions of Thom polynomials for A4(−) singularities have at most four parts. We simplify the system of equations that determines these polynomials and give a recursive description of Thom polynomials for A4(−) singularities. We also give Thom polynomials...