{"paper":{"title":"The volume of the space of holomorphic maps from S^2 to CP^k","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"J.M. Speight","submitted_at":"2010-03-29T14:50:17Z","abstract_excerpt":"Let $\\Sigma$ be a compact Riemann surface and $\\h_{d,k}(\\Sigma)$ denote the space of degree $d\\geq 1$ holomorphic maps $\\Sigma\\ra \\CP^k$. In theoretical physics this arises as the moduli space of charge $d$ lumps (or instantons) in the $\\CP^k$ model on $\\Sigma$. There is a natural Riemannian metric on this moduli space, called the $L^2$ metric, whose geometry is conjectured to control the low energy dynamics of $\\CP^k$ lumps. In this paper an explicit formula for the $L^2$ metric on of $\\h_{d,k}(\\Sigma)$ in the special case $d=1$ and $\\Sigma=S^2$ is computed. Essential use is made of the k\\\"ah"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5556","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}