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      Special Langrangian geometry and slightly deformed algebraic geometry (spLag and sdAG)

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          Abstract

          The special geometry of calibrated cycles, closely related to mirror symmetry among Calabi--Yau 3-folds, is itself a real form of a new subject, which we call slightly deformed algebraic geometry. On the other hand, both of these geometries are parallel to classical gauge theories and their complexifications. This article explains this parallelism, so that the appearance of invariants of new type in complexified gauge theory (see Donaldson--Thomas [D-T] and Thomas [T]) can be accompanied by analogous invariants in the theory of special Lagrangian cycles, for which the development is at present much more modest than in gauge theory. We discuss related geometric constructions, arising from mirror symmetry and symplectic geometry.

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          Calibrated geometries

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            The moduli spaces of vector bundles over an algebraic curve

            S. Ramanan (1973)
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              Author and article information

              Journal
              02 June 1998
              Article
              math/9806006
              d8fcaa94-db0d-4646-a084-89e750acdefe
              History
              Custom metadata
              Warwick preprint 1998
              45 pp., amstex, amsppt 2.1 (and epsf.tex for 2 inessential figures)
              math.AG

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