On the Picard group of low-codimension subvarieties Enrique ArrondoJorge Caravantes 14M07low codimensionPicard group We introduce a method to determine if $n$-dimensional smooth subvarieties of an ambient space of dimension at most $2n - 2$ inherits the Picard group from the ambient space (as it happens when the ambient space is a projective space, according to results of Barth and Larsen). As an application, we give an affirmative answer (up to some mild natural numerical conditions) when the ambient space is a Grassmannian of lines (thus improving results of Barth, Van de Ven and Sommese) or a product of two projective spaces of the same dimension. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3556 10.1512/iumj.2009.58.3556 en Indiana Univ. Math. J. 58 (2009) 1023 - 1050 state-of-the-art mathematics http://iumj.org/access/