{"paper":{"title":"Branched projective structures on a Riemann surface and logarithmic connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Indranil Biswas, Sorin Dumitrescu, Subhojoy Gupta","submitted_at":"2018-08-14T06:55:44Z","abstract_excerpt":"We study the set ${\\mathcal P}_S$ consisting of all branched holomorphic projective structures on a compact Riemann surface $X$ of genus $g \\geq 1$ and with a fixed branching divisor $S:= \\sum_{i=1}^d n_i\\cdot x_i$, where $x_i \\in X$. Under the hypothesis that $n_i=1$, for all $i$, with $d$ a positive even integer such that $d \\neq 2g-2$, we show that ${\\mathcal P}_S$ coincides with a subset of the set of all logarithmic connections with singular locus $S$, satisfying certain geometric conditions, on the rank two holomorphic jet bundle $J^1(Q)$, where $Q$ is a fixed holomorphic line bundle on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04555","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"}