Examples of K-unstable Fano manifolds

Examples of Non-symmetric Kähler-einstein Toric Fano Manifolds

Let us first recall our setting. In the toric case, there is a correspondence between n-dimensional nonsingular Fano varieties and ndimensional Fano polytopes, where the Fano varieties are biregular isomorphic if and only if the corresponding Fano polytopes are unimodularly equivalent. Here, given a lattice N of rank n, a Fano polytope Q ⊆ NR := N ⊗Z R is given as a lattice polytope containing ...

K-semistable Fano Manifolds with the Smallest Alpha Invariant

In this short note, we show that K-semistable Fano manifolds with the smallest alpha invariant are projective spaces. Singular cases are also investigated.

Mirror Symmetry and Fano Manifolds

Explicit Examples of Birationally Rigid Fano Varieties

We construct explicit examples of divisorially canonical Fano double spaces. Their direct products are birationally rigid Fano varieties with finitely many structures of a rationally connected fiber space. 2000 Math. Subj. Class. 14E05.

Examples of Manifolds

Definition 1 We now define what is meant by the statement that M is a d–dimensional manifold of class C (with 1 ≤ k ≤ ∞ — we shall deal almost exclusively with manifolds of class C). (a) Let M be a Hausdorff topological space. A coordinate system (or chart or coordinate patch) on M is a pair (U , φ) with U a connected open subset of M and φ a homeomorphism (a 1–1, onto, continuous function with...