Curves of genus seven that do not satisfy the Gieseker-Petri theorem
In the moduli space of curves of genus , , let be the locus of curves that do not satisfy the Gieseker-Petri theorem. In the genus seven case we show that is a divisor in .
Curves of genus ten on K3 surfaces
Curves of maximal genus in .
Curves of minimal genus on a general abelian variety
Curves on a double surface.
Let F be a smooth projective surface contained in a smooth threefold T, and let X be the scheme corresponding to the divisor 2F on T. A locally Cohen-Macaulay curve C included in X gives rise to two effective divisors on F, namely the largest divisor P contained in C intersection F and the curve R residual to C intersection F in C. We show that under suitable hypotheses a general deformation of R and P lifts to a deformation of C on X, and give applications to the study of Hilbert schemes of locally...
Curves on a ruled cubic surface.
For the general ruled cubic surface S (with a double line) in P3 = P3 sub k, k any algebraically closed field, we find necessary conditions for which curves on S can be the specialization of a flat family of curves on smooth cubics. In particular, no smooth curve of degree > 10 on S is such a specialization.
Curves on a smooth quadric.
We associate to every curve on a smooth quadric a polynomial equation that defines it as a divisor; this polynomial is defined through a matrix. In this way we can study several properties of these curves; in particular we can give a geometrical meaning to the rank of the matrix which defines the curve.
Curves on generic hypersurfaces
Curves on surfaces of degree 2r-... in Pr.
Curves on surfaces with multiple line.
Curves with finite turn
In this paper we study the notions of finite turn of a curve and finite turn of tangents of a curve. We generalize the theory (previously developed by Alexandrov, Pogorelov, and Reshetnyak) of angular turn in Euclidean spaces to curves with values in arbitrary Banach spaces. In particular, we manage to prove the equality of angular turn and angular turn of tangents in Hilbert spaces. One of the implications was only proved in the finite dimensional context previously, and equivalence of finiteness...
Curves with Invertible Hasse-Witt-Matrix.
Curves with only triple ramification
We show that the set of smooth curves of genus admitting a branched covering with only triple ramification points is of dimension at least . In characteristic two, such curves have tame rational functions and an analog of Belyi’s Theorem applies to them.
Cusp algebras.
Cuspidal local systems and graded Hecke algebras, I
Cuspidal Projections of Space Curves.
Cutting diagram method for systems of plane curves with base points
We develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne conjecture holds for systems with base points of equal multiplicity bounded by 42.
Cycle exceptionnel de l’éclatement d’un idéal définissant l’origine de et applications
Soit un idéal de définissant l’origine de . On donne une méthode explicite pour déterminer, après un choix convenable des générateurs de , le cycle de sous-jacent à la fibre exceptionnelle de l’éclatement de relativement à . On étudie également l’éclatement d’une famille équimultiple d’idéaux ponctuels paramétrée par un germe d’espace analytique complexe réduit.
Cycles de Hodge absolus et périodes des intégrales des variétés abéliennes. (Rédigé par J. L. Brylinski)
Cycles de Schubert et cohomologie equivariante de K/T.