Fano Varieties of K3-Type and IHS Manifolds

Unirationality of Fano Varieties

This note is an extension of the paper [HMP]. The main theorem of [HMP] states that a relatively smooth hypersurface (i.e. a hypersurface whose singular locus has sufficient large codimension with respect to its degree) is unirational. A mild modification can generalize this to complete intersections. As an application, we will show the Fano variety of a relatively smooth hypersurface is also u...

Gorenstein Toric Fano Varieties

We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for nonsingular toric Fano varieties. As applications we obtain new classification results, bounds of invariants and formulate conjectures concerning combinatoria...

Birationally Rigid Fano Varieties

We give a brief survey of the concept of birational rigidity, from its origins in the two-dimensional birational geometry, to its current state. The main ingredients of the method of maximal singularities are discussed. The principal results of the theory of birational rigidity of higher-dimensional Fano varieties and fibrations are given and certain natural conjectures are formulated.

the investigation of the relationship between type a and type b personalities and quality of translation

چکیده ندارد.

Mirror Symmetry and Fano Manifolds