In algebraic geometry, the Néron–Severi group of a variety is the group of divisors modulo algebraic equivalence; in other words it is the group of components of the Picard scheme of a …

Blow-ups: an example of a birational morphism 5 I realize now that I am starting to be sloppy about notation for divisors and their cor- responding invertible sheaves. For example, roman …

Apr 15, 2023 · The rank of $\mathrm {NS} (X)$ is the algebraic Betti number of the group of divisors on $X$, that is, the algebraic rank of $X$. This is also called the Picard number of the …

Feb 15, 2012 · The Neron-Severi group can also be described as the group of divisors on modulo algebraic equivalence ([3, V 1.7]). The behavior of the Neron-Severi group under a blow-up …

Elliptic surfaces give a very nice example of surfaces where algebraic equivalence and numeric equivalence coincide.

The Néron- Severi group NS(A) = Pic(A)/Pic0(A) is a free abelian group of finite rank ρ(A), called the Picard number of A. The group NS(A) appears often in the study of abelian varieties, but …

Feb 9, 2018 · Theorem (Néron, Severi). The Néron-Severi group of a surface is a finitely generated abelian group.

For an abelian variety A, the Neron-Severi group is torsion-free and (when tensored with Q) is isomorphic to the set of symmetric elements in the endomorphism algebra.

In this article we will show that such K3 surfaces do indeed exist. It follows from our main theorem.

LINES SAMUEL BOISSIμERE AND ALESSANDRA SARTI Abstract. For a binary quartic form Á without multiple factors, we classify the quartic K3 surfaces Á(x;y) = Á(z;t) whose N. eron …