Introduction. In this paper we discuss some recent results about maps of complex algebraic varieties. A contraction ϕ : X → Z is a proper surjective map of normal varieties with connected fibers. We will always assume that X, if not smooth, has mild singularities; in particular we assume that a rational multiple of the canonical sheaf, rK X , is a Cartier divisor. In this hypothesis the contrac...

Part 4. Biregular geometry 28 4.1. Fano-Mori contractions on a smooth n-fold with n ≤ 4 29 4.2. Fano-Mori contractions on a smooth n-fold with fibers of small dimension 34 4.3. The fibers of a Fano-Mori contraction 35 4.3.1. Using the vanishing theorem 35 4.3.2. Existence of a ladder for a fiber of a F-M contraction; horizontal slicing 37 4.3.3. Rational curves on the fiber of F-M contractions ...

Abstract This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, fixed point results for set-valued cone-contraction mappings. We theorem rational type cone-contractions spaces. Our extend improve given literature.

Abstract In this paper, we first introduce several new contractions by some auxiliary functions. Then establish φ -fixed point results for $(\gamma ,\psi ,\varphi ,\phi )$ ( γ , ψ φ ϕ ) contractions, rational...