997 research outputs found
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in
(possibly noncompact) toric varieties from the perspective of the
Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface in a toric
variety we construct a Landau-Ginzburg model which is SYZ mirror to the
blowup of along , under a positivity assumption.
This construction also yields SYZ mirrors to affine conic bundles, as well as a
Landau-Ginzburg model which can be naturally viewed as a mirror to . The
main applications concern affine hypersurfaces of general type, for which our
results provide a geometric basis for various mirror symmetry statements that
appear in the recent literature. We also obtain analogous results for complete
intersections.Comment: 83 pages; v2: added appendix discussing the analytic structure on
moduli of objects in the Fukaya category; v3: further clarifications in
response to referee report; v4: further clarifications throughout, especially
sections 4 and 7 and appendix A; added appendix B on the geometry of reduced
space
On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces
We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces
X and vector fields v which are K-stable in the sense of Berman-Nystrom and
therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide
some new examples of Fano threefolds admitting a Kahler-Ricci soliton.Comment: 21 pages, ancillary files containing calculations in SageMath; minor
correction
- …