Finiteness of 2-reflective lattices of signature (2,n)

2014/09/10 by Shouhei Ma, Ma, Shouhei · 1 citation
Mathematics · #11F22 #11F55 #14J28 #17B67 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1409.2969

openalex publication_date 2014/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A modular form for an even lattice L of signature (2,n) is said to be 2-reflective if its zero divisor is set-theoretically contained in the Heegner divisor defined by the (-2)-vectors in L. We prove that there are only finitely many even lattices with n>6 which admit 2-reflective modular forms. In particular, there is no such lattice in n>25 except the even unimodular lattice of signature (2,26). This proves a conjecture of Gritsenko and Nikulin in the range n>6.

Citations

• Reflective modular forms in algebraic geometry

Cited by

• Finiteness of Free Algebras of Modular Forms on Unitary Groups

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