{"arxiv_id":"hep-th/0009228","incoming":{"papers":28,"sentences":42,"groups":[{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1206.4281","title":"Stability and Fourier-Mukai transforms on elliptic fibrations","url":"/paper/1206.4281","section":"Application 2: pure codimension-1 sheaves","sentence":"Some of these results in this section resemble those obtained from the spectral construction of stable sheaves on elliptic fibrations (e.g. see [ref] ), as well as results obtained by Yoshioka, where he assumes the existence of a section for the fibration (see [ref] ).","intent_p":0.96,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1402.2653","title":"Box Graphs and Singular Fibers","url":"/paper/1402.2653","section":"Local models for fibers in codimension three","sentence":"If the Weierstrass coefficients $f$ and $g$ have multiplicities at $P_μ$ which exceed $4$ for $f$ and $6$ for $g$, then there is no desingularization of the Weierstrass model which is flat [ref] , which means that there would be tensionless strings in the low-energy theory.","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":4,"sentences":5,"quotes":[{"arxiv_id":"1306.3987","title":"Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors","url":"/paper/1306.3987","section":"Yukawa Couplings: Codimension Three","sentence":"The physics of this a non-flat fibration has been discussed in [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1907.05404","title":"Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States","url":"/paper/1907.05404","section":"Introduction","sentence":"In the context of F-theory, such fibrations have been systematically studied in [ref] for Kodaira fibers, with examples in codimension two and three appearing in [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"2108.07810","title":"Chiral matter multiplicities and resolution-independent structure in 4D F-theory models","url":"/paper/2108.07810","section":"Codimension-three $(4, 6)$ loci","sentence":"Many F-theory geometries contain $(4, 6)$ (or higher) singularities in the elliptic fibration over codimension-three loci in the base [ref] ; these are often associated with non-flat fibers in the resolution [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"1608.07555","title":"Multiple Fibrations in Calabi-Yau Geometry and String Dualities","url":"/paper/1608.07555","section":"A non-flat fibration $𝔼_4$","sentence":"Studying the physics associated to such fibrations [ref] is beyond the scope of this paper, although we will make a few comments in this direction at the end of this Section.","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":35},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/hep-th/0009228"}}