In this paper we will describe an approach to mirror symmetry for appropriate one-dimensional DM stacks of arithmetic genus g ≤ 1, called tcnc curves, which was developed by the author with Treumann and Zaslow in Sibilla et al. (Ribbon Graphs and Mirror Symmetry I, arXiv:1103.2462). This involves introducing a conjectural sheaf-theoretic model for the Fukaya category of punctured Riemann surfaces. As an application, we will investigate derived equivalences of tcnc curves, and generalize classic results of Mukai on dual abelian varieties (Mukai, Nagoya Math. J. 81, 153–175, 1981).
Mirror Symmetry in Dimension 1 and Fourier–Mukai Transforms / Sibilla, Nicolò. - (2014), pp. 407-428.
Mirror Symmetry in Dimension 1 and Fourier–Mukai Transforms
Nicolò Sibilla
2014-01-01
Abstract
In this paper we will describe an approach to mirror symmetry for appropriate one-dimensional DM stacks of arithmetic genus g ≤ 1, called tcnc curves, which was developed by the author with Treumann and Zaslow in Sibilla et al. (Ribbon Graphs and Mirror Symmetry I, arXiv:1103.2462). This involves introducing a conjectural sheaf-theoretic model for the Fukaya category of punctured Riemann surfaces. As an application, we will investigate derived equivalences of tcnc curves, and generalize classic results of Mukai on dual abelian varieties (Mukai, Nagoya Math. J. 81, 153–175, 1981).| File | Dimensione | Formato | |
|---|---|---|---|
|
cetraro proc.pdf
non disponibili
Tipologia:
Documento in Post-print
Licenza:
Copyright dell'editore
Dimensione
345.22 kB
Formato
Adobe PDF
|
345.22 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
