Involutions, Humbert surfaces, and divisors on a moduli space

  • Steven H. Weintraub

    Lehigh University, Bethlehem, USA


Let M*2 be the Igusa compactification of the Siegel modular variety of degree 2 and level 2. In earlier work with R. Lee, we carefully investigated this variety. Subvarieties Dℓ (compactification divisors) and _H_Δ (Humbert surface of discriminant 1) play a prominent role in its structure; in particular their fundamental classes span _H_4(M*2; ℤ). We return to this variety and consider another class of subvarieties Kh (Humbert surfaces of degree 4), which we investigate with the help of involutions on M*2. We carefully describe these subvarieties and consider the representations of their fundamental classes in terms of the fundamental classes of the subvarieties Dℓ and _H_Δ. The space M*2 is also known in a different context. It can also be described as the space _M_0; 6 of stable curves of genus 2 with ordered Weierstrass points. In this context the divisors Kh are what have come to be known as Keel-Vermeire divisors.

Cite this article

Steven H. Weintraub, Involutions, Humbert surfaces, and divisors on a moduli space. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 4, pp. 415–440

DOI 10.4171/RLM/581