1,518 research outputs found
Constructing projective varieties in weighted flag varieties
We compute the Hilbert series of general weighted flag varieties and discuss
a computer-aided method to determine their defining equations. We apply our
results to weighted flag varieties coming from the Lie groups of type G_2 and
GL(6), to construct some families of polarised projective varieties in
codimensions 8 and 6, respectively.Comment: 17 pages, 1 figur
Examples of abelian surfaces with everywhere good reduction
We describe several explicit examples of simple abelian surfaces over real
quadratic fields with real multiplication and everywhere good reduction. These
examples provide evidence for the Eichler-Shimura conjecture for Hilbert
modular forms over a real quadratic field. Several of the examples also support
a conjecture of Brumer and Kramer on abelian varieties associated to Siegel
modular forms with paramodular level structures.Comment: 26 pages. Final version (to appear in Mathematische Annalen
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