We consider the Siegel modular variety of genus 2 and a p-integral model of
it for a good prime p>2, which parametrizes principally polarized abelian
varieties of dimension two with a level structure. We consider cycles on this
model which are characterized by the existence of certain special
endomorphisms, and their intersections. We characterize that part of the
intersection which consists of isolated points in characteristic p only.
Furthermore, we relate the (naive) intersection multiplicities of the cycles at
isolated points to special values of derivatives of certain Eisenstein series
on the metaplectic group in 8 variables.
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