Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 1, pp. 9-26 (2002)

Picard Groups of Deligne-Lusztig Varieties - with a View toward Higher Codimensions

Soren Have Hansen

Centre for Mathematical Physics and Stochastics, Department of Mathematical Sciences, University of Aarhus, DK-8000 Aarhus C, Denmark, e-mail: shave@imf.au.dk

Abstract: For a Deligne-Lusztig variety $\bar X (w)$ arising from one of the classical (possibly twisted) groups, we show that the Picard group of $\bar X(w)$ is generated by the finitely many Deligne-Lusztig subvarieties of $\bar X (w)$. It is conjectured that this more generally should hold in any codimension, and a good deal of supporting evidence for this claim is presented.

Keywords: algebraic geometry, algebraic groups, Deligne-Lusztig varieties, Picard (and Chow) groups

Classification (MSC2000): 14M15,14C25

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