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The Quarterly Journal of Mathematics Advance Access originally published online on February 17, 2006
The Quarterly Journal of Mathematics 2006 57(4):539-554; doi:10.1093/qmath/hal004
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© The author 2006. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

FERMAT COVERS, FERMAT HYPERSURFACES AND ABELIAN VARIETIES OF FERMAT TYPE

Chad Schoen {dagger}

Department of Mathematics, Duke University, Box 90320, Durham, NC 27708-0320, USA


  Abstract

Albanese maps for smooth projective models of a class of Abelian covers of projective space branched along particular hyperplane arrangements are studied. In some cases it is shown that the image of the Albanese map gives a cycle in the Albanese variety which is not numerically equivalent to a linear combination of intersections of divisors. Smooth projective varieties with this property are said to be Albanese exotic. Few concrete examples of such varieties are known.


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