Ternary quartics and 3-dimensional commutative algebras.
The Abel-Jacobi map for cubic threefold and periods of Fano threefolds of degree 14.
The Apery algorithm for a plane singularity with two branches.
The dimension of the Chow variety of curves
The equations of space curves on a quadric.
The homogeneous ideals of curves in a double plane have been studied by Chiarli, Greco, Nagel. Completing this work we describe the equations of any curve that is contained in some quadric. As a consequence, we classify the Hartshorne-Rao modules of such curves.
The Genus of Curves in P4 and P5.
The Genus of Curves in P4 verifying certain Flag conditions.
The growth rate of the number of classes of real plane algebraic curves with the growth of the degree.
The Hilbert Function of curves on certain smooth quartic surfaces.
The Hilbert Scheme of Buchsbaum space curves
We consider the Hilbert scheme of space curves with homogeneous ideal and Rao module . By taking suitable generizations (deformations to a more general curve) of , we simplify the minimal free resolution of by e.g making consecutive free summands (ghost-terms) disappear in a free resolution of . Using this for Buchsbaum curves of diameter one ( for only one ), we establish a one-to-one correspondence between the set of irreducible components of that contain and a set of minimal...
The Hilbert scheme of space curves of small diameter
This paper studies space curves of degree and arithmetic genus , with homogeneous ideal and Rao module , whose main results deal with curves which satisfy (e.g. of diameter, ). For such curves we find necessary and sufficient conditions for unobstructedness, and we compute the dimension of the Hilbert scheme, , at under the sufficient conditions. In the diameter one case, the necessary and sufficient conditions coincide, and the unobstructedness of turns out to be equivalent to the...
The Hilbert schemes of degree three curves
The irregularity of ruled surfaces in three dimensional projective space.
Let S be a ruled surface in P3 with no multiple generators. Let d and q be nonnegative integers. In this paper we determine which pairs (d,q) correspond to the degree and irregularity of a ruled surface, by considering these surfaces as curves in a smooth quadric hypersurface in P5.
The Number of Twisted Cubic Curves on the General Quintic Threefold.
The Tangent Surface of a rational Algebraic Space Curve.
Théorèmes divers concernant les systèmes de coniques représentés par deux caractéristiques
Tropical resultants for curves and stable intersection.