Galois embedding of algebraic variety and its application to abelian surface
Gaussian maps for double coverings.
General Components of the Noether-Lefschetz Locus and their Density in the Space of all Surfaces.
Generalized polar varieties and an efficient real elimination
Let be a closed algebraic subvariety of the -dimensional projective space over the complex or real numbers and suppose that is non-empty and equidimensional. In this paper we generalize the classic notion of polar variety of associated with a given linear subvariety of the ambient space of . As particular instances of this new notion of generalized polar variety we reobtain the classic ones and two new types of polar varieties, called dual and (in case that is affine) conic. We show that...
Générateurs explicites du groupe de Chow du schéma de Hilbert des cubiques de IP(3, C).
Generic Curves of Small Genus in IP3 are of Maximal Rank.
Genre des courbes algébriques dans l'espace projectif
Geometric representations of interacting maps.
Geometric structures on the complement of a projective arrangement
Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (= finite union of hyperplanes) whose Levi-Civita connection is of Dunkl type. Interesting examples are obtained from the arrangements defined by finite complex reflection groups. We determine a parameter interval for which the metric is locally of Fubini-Study type, flat, or complex-hyperbolic. We find a finite subset of this interval for...
Geometry of superficial elements
Grassmann defective surfaces
A projective variety is -defective if the Grassmannian of lines contained in the span of independent points on has dimension less than the expected one. In the present paper, which is inspired by classical work of Alessandro Terracini, we prove a criterion of -defectivity for algebraic surfaces and we discuss its applications to Veronese embeddings and to rational normal scrolls.
Green's generic syzygy conjecture for curves of even genus lying on a K3 surface
We consider the generic Green conjecture on syzygies of a canonical curve, and particularly the following reformulation thereof: For a smooth projective curve of genus in characteristic 0, the condition is equivalent to the fact that . We propose a new approach, which allows up to prove this result for generic curves of genus and gonality in the range
Gromov–Witten invariants for mirror orbifolds of simple elliptic singularities
We consider a mirror symmetry of simple elliptic singularities. In particular, we construct isomorphisms of Frobenius manifolds among the one from the Gromov–Witten theory of a weighted projective line, the one from the theory of primitive forms for a universal unfolding of a simple elliptic singularity and the one from the invariant theory for an elliptic Weyl group. As a consequence, we give a geometric interpretation of the Fourier coefficients of an eta product considered by K. Saito.