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- W1554486667 abstract "In a suitable regime of superstring theory, D-branes in a Calabi-Yau space and their most fundamental behaviors can be nicely described mathematically through morphisms from Azumaya spaces with a fundamental module to that Calabi-Yau space. In the earlier work [L-L-S-Y] (D(2): arXiv:0809.2121 [math.AG], with Si Li and Ruifang Song) from the project, we explored this notion for the case of D1-branes (i.e. D-strings) and laid down some basic ingredients toward understanding the notion of D-string world-sheet instantons in this context. In this continuation, D(10), of D(2), we move on to construct a moduli stack of semistable morphisms from Azumaya nodal curves with a fundamental module to a projective Calabi-Yau 3-fold $Y$. In this Part I of the note, D(10.1), we define the notion of twisted central charge $Z$ for Fourier-Mukai transforms of dimension 1 and width [0] from nodal curves and the associated stability condition on such transforms and prove that for a given compact stack of nodal curves $C_{cal M}/{cal M}$, the stack $FM^{1,[0];Zss}_{C_{cal M}/{cal M}}(Y,c)$ of $Z$-semistable Fourier-Mukai transforms of dimension 1 and width [0] from nodal curves in the family $C_{cal M}/{cal M}$ to $Y$ of fixed twisted central charge $c$ is compact. For the application in the sequel D(10.2), $C_{cal M}/{cal M}$ will contain $C_{bar{cal M}_g}/bar{cal M}_g$ as a substack and $FM^{1,[0];Zss}_{C_{cal M}/{cal M}}(Y,c)$ in this case will play a key role in defining stability condition for morphisms from arbitrary Azumaya nodal curves (with the underlying nodal curves not necessary in the family $C_{cal M}/{cal M}$) to $Y$." @default.
- W1554486667 created "2016-06-24" @default.
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- W1554486667 date "2013-02-08" @default.
- W1554486667 modified "2023-10-18" @default.
- W1554486667 title "A mathematical theory of D-string world-sheet instantons, I: Compactness of the stack of $Z$-semistable Fourier-Mukai transforms from a compact family of nodal curves to a projective Calabi-Yau 3-fold" @default.
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- W1554486667 doi "https://doi.org/10.48550/arxiv.1302.2054" @default.
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