Cones of Heegner divisors
Jan Hendrik Bruinier, Martin M\"oller
TL;DR
This paper proves that the cone of primitive Heegner divisors is finitely generated for many orthogonal Shimura varieties, including moduli spaces of polarized K3-surfaces, using modular form coefficient growth.
Contribution
It establishes finite generation of the cone of primitive Heegner divisors for various orthogonal Shimura varieties, a significant advancement in understanding their geometric structure.
Findings
Finite generation of the cone of primitive Heegner divisors for many orthogonal Shimura varieties.
Application to the moduli space of polarized K3-surfaces.
Use of modular form coefficient growth in the proof.
Abstract
We show that the cone of primitive Heegner divisors is finitely generated for many orthogonal Shimura varieties, including the moduli space of polarized K3-surfaces. The proof relies on the growth of coefficients of modular forms.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Advanced Topics in Algebra