Morphisms from Azumaya prestable curves with a fundamental module to a projective variety: Topological D-strings as a master object for curves

Details Morphisms from Azumaya prestable curves with a fundamental module to a projective variety: Topological D-strings as a master object for curves Morphisms from Azumaya prestable curves with a fundamental module to a projective variety: Topological D-strings as a master object for curves

2008-09-12

arxiv.org/abs/0809.2121v1

Mathematics

Algebraic Geometry

30 pages

Scientific paper

This is a continuation of our study of the foundations of D-branes from the viewpoint of Grothendieck in the region of the related Wilson's theory-space where "branes" are still branes. In this work, we focus on D-strings and construct the moduli stack of morphisms from Azumaya prestable curves $C^{Az}$ with a fundamental module ${\cal E}$ to a fixed target $Y$ of a given combinatorial type. Such a morphism gives a prototype for a Wick-rotated D-string of B-type on $Y$, following the Polchinski-Grothendieck Ansatz, and this stack serves as a ground toward a mathematical theory of topological D-string world-sheet instantons.

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