Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves

@article{Auroux2006MirrorSF,
  title={Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves
},
  author={D. Auroux and L. Katzarkov and D. Orlov},
  journal={Inventiones mathematicae},
  year={2006},
  volume={166},
  pages={537-582}
}
We study homological mirror symmetry for Del Pezzo surfaces and their mirror Landau-Ginzburg models. In particular, we show that the derived category of coherent sheaves on a Del Pezzo surface Xk obtained by blowing up ℂℙ2 at k points is equivalent to the derived category of vanishing cycles of a certain elliptic fibration Wk:Mk→ℂ with k+3 singular fibers, equipped with a suitable symplectic form. Moreover, we also show that this mirror correspondence between derived categories can be extended… Expand
169 Citations

Figures from this paper

Homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces
  • 17
  • Highly Influenced
  • PDF
Toric systems and mirror symmetry
  • 3
  • PDF
On exceptional collections of line bundles and mirror symmetry for toric Del-Pezzo surfaces
  • 4
  • PDF
Homological Mirror Symmetry for Toric del Pezzo Surfaces
  • 41
  • PDF
Explicit equations for mirror families to log Calabi-Yau surfaces
  • 3
  • PDF
Monodromy of Fukaya-Seidel categories mirror to toric varieties
  • 6
Mirror Symmetry for Lattice Polarized del Pezzo Surfaces
  • 6
  • Highly Influenced
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 29 REFERENCES
More about vanishing cycles and mutation
  • 129
  • PDF
Blowing up non-commutative smooth surfaces
  • 114
  • PDF
Exceptional Sheaves on del Pezzo Surfaces
  • 82
Homological Algebra of Mirror Symmetry
  • 1,135
  • PDF
D branes in Landau-Ginzburg models and algebraic geometry
  • 230
  • PDF
...
1
2
3
...