6,994 research outputs found
Birational geometry via moduli spaces
In this paper we connect degenerations of Fano threefolds by projections.
Using Mirror Symmetry we transfer these connections to the side of
Landau--Ginzburg models. Based on that we suggest a generalization of
Kawamata's categorical approach to birational geometry enhancing it via
geometry of moduli spaces of Landau--Ginzburg models. We suggest a conjectural
application to Hasset--Kuznetsov--Tschinkel program based on new nonrationality
"invariants" we consider --- gaps and phantom categories. We make several
conjectures for these invariants in the case of surfaces of general type and
quadric bundles.Comment: arXiv admin note: text overlap with arXiv:1405.295
Weierstrass models of elliptic toric K3 hypersurfaces and symplectic cuts
We study elliptically fibered K3 surfaces, with sections, in toric Fano
threefolds which satisfy certain combinatorial properties relevant to
F-theory/Heterotic duality. We show that some of these conditions are
equivalent to the existence of an appropriate notion of a Weierstrass model
adapted to the toric context. Moreover, we show that if in addition other
conditions are satisfied, there exists a toric semistable degeneration of the
elliptic K3 surface which is compatible with the elliptic fibration and
F-theory/Heterotic duality.Comment: References adde
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