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These sets were introduced recently by Voisin and she showed that $\\dim V_k(A) \\leq k-1$ and $V_k(A)$ is countable for a very general abelian variety of dimension at least $2k-1$.\n  We study in particular the locus $\\mathcal V_{g,2}$ in the moduli space of abelian varieties of dimension $g$ with a fixed polarization, where $V_2(A)$ is positive dimensional. We prove that "},"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":"2004.06907","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-15T07:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"b3912b119b06fb6012ded5a5e20109d10880b7560feac02cc5813301a0e62be8","abstract_canon_sha256":"0992a5ce8d8066c5debd3e1c6ad36ff8e701231f7160b039156de90f1b8f75da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:05:06.634542Z","signature_b64":"7opFGzws4Ci3VfsGgYO/WLk5hN2FvaP+P05oMi/giPBVaqSvso2JAsD702b4TXJIP5H0NUylyOhPEAPQ8Gn6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e91621f8eed5f6fefd9317a370e92ecbc29d8561804970855e24361749f109e5","last_reissued_at":"2026-07-05T02:05:06.634139Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:05:06.634139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the dimension of Voisin sets in the moduli space of abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"E. Colombo, G.P. Pirola, J.C. Naranjo","submitted_at":"2020-04-15T07:03:20Z","abstract_excerpt":"We study the subsets $V_k(A)$ of a complex abelian variety $A$ consisting in the collection of points $x\\in A$ such that the zero-cycle $\\{x\\}-\\{0_A\\}$ is $k$-nilpotent with respect to the Pontryagin product in the Chow group. These sets were introduced recently by Voisin and she showed that $\\dim V_k(A) \\leq k-1$ and $V_k(A)$ is countable for a very general abelian variety of dimension at least $2k-1$.\n  We study in particular the locus $\\mathcal V_{g,2}$ in the moduli space of abelian varieties of dimension $g$ with a fixed polarization, where $V_2(A)$ is positive dimensional. 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