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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.7117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-26T15:07:36Z","cross_cats_sorted":[],"title_canon_sha256":"f7c2b198f21b0e4ba9fe10171ad54165d83690939fb30010d76d7b5c50089a2e","abstract_canon_sha256":"bdfb6cdcc3eae7d4c84337437c83899abeafd5cf43809baf89ac6f56d2d041e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:31.015780Z","signature_b64":"g7zxlJ/JR9ZcG8Mzs2QoXsXz/l0mY6htbLFnYpTMrHU+ADTcT2vm9Y0mxKFYJTWD0XbvROHqjp87ozpmUS7QCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25c3647c1b9859c7797c38eec27147ae6c18968ad425f8c33694b78543593af8","last_reissued_at":"2026-05-18T01:34:31.015348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:31.015348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathbb{P}^2$. 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