Related papers: Nonrationality of a generic cubic fourfold
This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.
We prove that the intermediate Jacobian of the Klein quartic $3$-fold $X$ is not isomorphic, as a principally polarized abelian variety, to a product of Jacobians of curves. As corollaries we deduce (using a criterion of Clemens-Griffiths)…
A false application of Proposition 4.10 causes a mistake in the proof of Corollary 4.11
The paper has benn withdrawn because the computation of the external virial contains an error which invalidate the main result.
A very short note, explaining the error in the original paper, which renders its central result incorrect.
We generalize Tennenbaum's geometric proof of the irrationality of sqrt(2) to sqrt(n) for n = 3, 5, 6 and 10. Modified version published in Mathematics Magazine \textbf{85} (2012), no. 2, 110--114.
This paper has been withdrawn by the author(s), due a crucial sign error in conclusion .
We generalize L.J. Mordell's construction of cubic surfaces for which the Hasse principle fails.
The paper is withdrawn. The proof has an error and it requires a different approach.
This paper has been withdrawn as the proof of Lemma 4.1 is incomplete.
Let $X_4\subset\mathbb{P}^{n+1}$ be a quartic hypersurface of dimension $n\geq 4$ over an infinite field $k$. We show that if either $X_4$ contains a linear subspace $\Lambda$ of dimension $h\geq \max\{2,\dim(\Lambda\cap…
Segre proved that a smooth cubic surface over Q is unirational iff it has a rational point. We prove that the result also holds for cubic hypersurfaces over any field, including finite fields.
This paper was withdrawn by the author because severe errors were discovered.
This paper has been withdrawn by the author because eq.(4) and those subsequent are incorrect.
In the first part of this paper we will prove the Voevodsky's nilpotence conjecture for smooth cubic fourfolds and ordinary generic Gushel-Mukai fourfolds. Then, making use of noncommutative motives, we will prove the Voevodsky's nilpotence…
This paper has been withdrawn due to a crucial theoretical error.
This paper has been withdrawn because of serious errors.
This paper is cancelled
There are three types of involutions on a cubic fourfold; two of anti-symplectic type, and one symplectic. Here we show that cubics with involutions exhibit the full range of behaviour in relation to rationality conjectures. Namely, we show…
This paper has been withdrawn by the author, due to a significant error in section 4.3.1.