1999/02/04 by Andrei Tyurin, Tyurin, Andrei
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/9902027
latex2e with amsmath, amsfonts, amssymb, theorem, 53 pages
arxiv created 1999/02/04 · arxiv updated 2009/11/30
After the appearance of my preprint [T3] (Special Lagrangian geometry and slightly deformed algebraic geometry (spLag and sdAG), Warwick preprint 22/1998, alg-geom/9806006, 54 pp.). I received an e-mail from Cumrun Vafa, who recognized that the subject is closely related to that of his preprint [V] (Extending mirror conjecture to Calabi-Yau with bundles, hep-th/9804131, 7 pp.). This text started out as an e-mail ``reply'' to his letter. All the constructions we propose have well known ``spectral curve'' prototypes (see for example Friedman and other [FMW], Bershadsky and other [BJPS] and a number of others). Roughly speaking, our constructions are the spectral curve construction plus the phase geometry described in [T3]. So this text should really come before [T3], as motivation for the development of the geometry of the phase map in [T3].