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Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
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Calculations of Pic^0, Pic, NS of surfaces
For surfaces in $\mathbb{P}^3$ of degree at most 3 the calculation of $Pic(X)$ is relatively easy: In this case $X$ is rational, hence $NS(X)$ modulo torsion equals $H^2(X,\mathbb{Z})$.
(If you work …