Related papers: Nonrationality of a generic cubic fourfold

An arithmetic method of proving the irrationality of smooth projective 3-folds is described, using reduction modulo $p$. It is illustrated by an application to a cubic threefold, for which the hypothesis that its intermediate Jacobian is…

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

This paper has been withdrawn by the author due to a crucial error.

We prove the termination of 4-fold canonical flips.

We complete the proof of the fact that all principal permutation classes generated by a pattern longer than two have a nonrational generating function.

In their IZA Discussion Paper 10247, Johansson and Lee claim that the main result (Proposition 3) in Abbring and Van den Berg (2003b) does not hold. We show that their claim is incorrect. At a certain point within their line of reasoning,…

We prove the non-rationality of a double cover of $\mathbb{P}^{n}$ branched over a hypersurface $F\subset\mathbb{P}^{n}$ of degree $2n$ having isolated singularities such that $n\ge 4$ and every singular points of the hypersurface $F$ is…

A strong form of the Manin-Peyre conjecture with a power saving error term is proved for a certain cubic fourfold.

This paper has been withdrawn by the authors, due to a crucial error.

We prove that every Hassett's Noether-Lefschetz divisor of special cubic fourfolds contains a union of three codimension-two subvarieties, parametrizing rational cubic fourfolds, in the moduli space of smooth cubic fourfolds.

The main goal of this work is to prove that every entire curve in a generic hypersurface of degree greater than or equal to 593 in the complex projective space of dimension 4 is algebraically degenerated i.e contained in a proper…

The defect of a cubic threefold $X$ with isolated singularities is a global invariant that measures the failure of $\mathbb{Q}$-factoriality. We compute the defect for such cubics in terms of topological data about the curve of lines…

In this paper we investigate the degrees of irrationality of degenerations of $\epsilon$-lc Fano varieties of arbitrary dimensions. We show that given a generically $\epsilon$-lc klt Fano fibration $X\to Z$ of dimension $d$ over a smooth…

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

We prove the universal triviality of the third unramified cohomology group of a very general complex cubic fourfold containing a plane. The proof uses results on the unramified cohomology of quadrics due to Kahn, Rost, and Sujatha.

We show that rationality does not specialize in flat projective families of complex fourfolds with terminal singularities. This answers a question of Totaro, who established the analogous result in all dimensions greater than 4.

We prove that the generalized rational blowdown, a surgery on smooth 4-manifolds, can be performed in the symplectic category.

The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.

This paper has been withdrawn because Proposition 2.2 (c) is false. This invalids the main results of section 2 and 3. We thank A. Canonaco for pointing us the error.

The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…