The absence of stable Schottky forms

Details The absence of stable Schottky forms The absence of stable Schottky forms

2011-12-28

arxiv.org/abs/1112.6137v1

Mathematics

Algebraic Geometry

Scientific paper

Let $A_g^S$ be the Satake compactification of the moduli space $A_g$ of principally polarized abelian $g$-folds and $M_g^S$ the closure of the image of the moduli space $M_g$ of genus $g$ curves in $A_g$ under the Jacobian morphism. Then $A_g^S$ lies in the boundary of $A_{g+m}^S$ for any $m$. We prove that $M_{g+m}^S$ and $A_g^S$ do not meet transversely in $A_{g+m}^S$, but rather that their intersection contains the $m$th order infinitesimal neighbourhood of $M_g^S$ in $A_g^S$. We deduce that there is no non-trivial stable Siegel modular form that vanishes on $M_g$ for every $g$. In particular, given two inequivalent positive even unimodular quadratic forms $P$ and $Q$, there is a curve whose period matrix distinguishes between the theta series of $P$ and $Q$.

Affiliated with

Also associated with

No associations

Rating

The absence of stable Schottky forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The absence of stable Schottky forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The absence of stable Schottky forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-32579