On the Picard number of a complex projective variety

Many interesting cases from that classification, and especially among the prime Fano manifolds of index one, are obtained by taking suitable sections (mostly linear sections) of

F or example, let's onsider again the task of representing all numbers from 0 through deimal 999,999: in base 10 this obviously requires a width of six digits, so that.. rw = 60

We first describe the general situation for a prime divisor D in a Mori dream space Lemma 2.6, and then consider the case of a special Mori program for −D where D is a prime divisor

The proof is based on a result on Prym varieties stated in [12], which asserts that a very generic Prym variety, of dimension greater or equal to 4, of a ramified double covering is

is a canonical decomposition of the collineation group 0152 == G fG with respect to its reduced symplectic structure (cf. III below). They play a very useful role

shown is that for a general hypersurface X of high degree, the image of the Abel- Jacobi is no larger than what is required if the Hodge Conjecture is going to

1. either injective or surjective) for a general choice of C and L in the range where the Brill–Noether number is nonnegative. The original formulation of the conjecture is due

Key words: Algebraic varieties of general type — Rational maps — Canonical bundle and pluricanonical embeddings — Chern classes — Finiteness theorems of de Franchis - Severi type