{"paper":{"title":"Stability for Line Bundles and Deformed Hermitian-Yang-Mills Equation on Some Elliptic Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jason Lo, Shing-Tung Yau, Tristan C. Collins, Yun Shi","submitted_at":"2023-06-09T01:49:21Z","abstract_excerpt":"We study the twisted ampleness criterion due to Collins, Jacob and Yau on surfaces, which is equivalent to the existence of solutions to the deformed Hermitian-Yang-Mills (dHYM) equation. When $X$ is a Weierstrass elliptic K3 surface, and $\\omega$ an ample class such that $\\omega$ lies in the span of a section class and the fiber class, we show that for a class of line bundles $L$ with fiber degree 1 and $\\omega c_1(L)>0$, the twisted ampleness of $L$ respect to $\\omega$, always implies the $\\sigma_{\\omega, 0}$-stability (Bridgeland stability) of $L$. This answers a question by Collins and Yau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05620","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.05620/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}