{"paper":{"title":"Affine pavings for moduli spaces of pure sheaves on $\\mathbb{P}^2$ with degree $\\leq 5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yao Yuan","submitted_at":"2013-12-26T15:07:36Z","abstract_excerpt":"Let $M(d,r)$ be the moduli space of semistable sheaves of rank 0, Euler characteristic $r$ and first Chern class $dH (d>0)$, with $H$ the hyperplane class in $\\mathbb{P}^2$. By previous work, we gave an explicit description of the class $[M(d,r)]$ of $M(d,r)$ in the Grothendieck ring of varieties for $d\\leq 5$ and $g.c.d(d,r)=1$. In this paper we compute the fixed locus of $M(d,r)$ under some $(\\mathbb{C}^{*})^2$-action and show that $M(d,r)$ admits an affine paving for $d\\leq 5$ and $g.c.d(d,r)=1$. We also pose a conjecture that for any $d$ and $r$ coprime to $d$, $M(d,r)$ would admit an affi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7117","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"}