Rational curves and bounds on the Picard number of Fano manifolds.

As a corollary we prove very weak bounded negativity for smooth curves on surfaces with .X / > 0..

In this section, by using classical deformation theory of plane curve singu- larities, we will find sufficient conditions for the existence of curves with A k -singularities on

The Hilbert scheme of rational, smooth and irreducible curves C of degree d on a general quintic threefold in P 4 is finite, nonempty and reduced, so each curve is embedded with

In particular, the general members of all the moduli spaces occurring in Corollary 1.2 are extendable to an Enriques–Fano threefold (X, L ) such that the morphism ϕ L defined by |L|

The Hilbert scheme of rational, smooth and irreducible curves C of degree d on a general quintic threefold in P 4 is finite, nonempty and reduced, so each curve is embedded with

We prove that the Koras-Russell cubic threefold is not diffeomorphic to Euclidean space as a smooth manifold but isomorphic to affine three space as a complex algebraic

The main idea is to first establish the results in the case where X is smooth projective, where good properties can be utilised. Part 1) is proven in the course of this process. If X

Echoing Schumpeter, Achen and Bartels (2016) argue that popular notions of government responsiveness to public preferences – what they refer to as “the folk theory” of