Involutions, Humbert surfaces, and divisors on a moduli space

  • Steven H. Weintraub

    Lehigh University, Bethlehem, USA

Abstract

Let 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 (compactification divisors) and (Humbert surface of discriminant 1) play a prominent role in its structure; in particular their fundamental classes span . We return to this variety and consider another class of subvarieties (Humbert surfaces of degree 4), which we investigate with the help of involutions on . We carefully describe these subvarieties and consider the representations of their fundamental classes in terms of the fundamental classes of the subvarieties and . The space is also known in a different context. It can also be described as the space of stable curves of genus 2 with ordered Weierstrass points. In this context the divisors 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