Cutting out arithmetic Teichmueller curves in genus two via Theta\n functions

2015/04/02 by André Kappes, Martin Möller, Kappes, André +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.1504.00470

openalex publication_date 2015/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the class of arithmetic genus two Teichmueller curves in the\nPicard group of pseudo-Hilbert modular surfaces, distinguished according to\ntheir torsion order and spin invariant. As an application, we compute the\nnumber of genus two square-tiled surfaces with these invariants. The main\ntechnical tool is the computation of divisor classes of Hilbert Jacobi forms on\nthe universal abelian surface over the pseudo-Hilbert modular surface.\n

Related

• The arithmetic of genus two curves
• Deligne-Mumford compactification of the real multiplication locus and Teichmueller curves in genus three
• Teichmueller curves in genus three and just likely intersections in G_mⁿ x G_aⁿ
• Variations of Hodge structures of a Teichmueller curve
• Prime arithmetic Teichmuller discs in H(2)