Abstract:
In the talk we will discuss several results related to
construction of new examples of prime Fano varieties and mirror
symmetry for Fano varieties.
We will describe the structure of classification of smooth Fano
weighted complete intersections, and discuss the existence of
Landau–Ginzburg models of Givental's type for them. We will show
that for any smooth Fano threefold the polarisation of its general
anticanonical section by restriction of Picard lattice is
mirror-dual to the polarisation of a general fibre of the
Landau–Ginzburg model for the Fano threefold by monodromy
invariants. If time allows, we will also discuss other topics
related to weighted complete intersections: complete intersections
in weighted Grassmannians and higher-dimensional versions of Belyi's
theorem.
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