Related papers: Nonrationality of a generic cubic fourfold
In this paper, we present the invalidities of the results in [3], because of their definition of a semi-invariant submanifold of an almost complex contact metric manifold is not true .
This paper has been withdrawn by the author due to a crucial sign error in equation 1.
We show geometrically that $\sqrt n$ is irrational for $n=3,5,7$ by adapting Tennenbaum's geometric proof that $\sqrt 2$ is irrational. We also show that this method cannot be used to prove the irrationality of $\sqrt n$ for a bigger $n$.
The $\mathbb{Q}$-factoriality of a nodal quartic 3-fold implies its non-rationality. We prove that a nodal quartic 3-fold with at most 8 nodes is $\mathbb{Q}$-factorial, and we show that a nodal quartic 3-fold with 9 nodes is not…
This paper is withdrawn.
This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.
We give a simple proof of the non-rationality of the Fano threefold defined by the equations \Sigma x_i = \Sigma x_i^2 = \Sigma x_i^3 = 0 in P^6 .
This paper has been withdrawn by the author, due to an error in the inequality after the inequality (31).
This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.
Cubic forms $C$ are constructed in the work of R. Aguilar, M. Green and P. Griffiths to establish the generic global Torelli theorem for Fano-K3 pairs $(X,Y)$, where $X: F=0$ is a cubic threefold in $\mathbb{P}^4$ and $Y\in|-K_X|$ is an…
This paper has been withdrawn by the authors due to the crucial wrong assumption following Eq. 9.
For any irrational theta and rational number p/q such that q|qtheta-p|<1, a projection e of trace q|qtheta-p| is constructed in the the irrational rotation algebra A_theta that is invariant under the Fourier transform. (The latter is the…
We establish a rigidity result for the critical points, with boundary, of a four dimensional Willmore energy. These critical points satisfy a 4-Willmore equation which is a sixth order nonlinear elliptic partial differential equation. We…
The main result of this paper, as previously presented to arxiv, was incorrect. See the full text for details and for reference to the remaining results.
By leveraging the physics of the Higgs branch, we argue that the conformal central charges $a$ and $c$ of an arbitrary 4d $N=2$ superconformal field theory (SCFT) are rational numbers. Our proof of the rationality of $c$ is conditioned on a…
We prove, for many cuspidal automorphic representations for GSp(4), that the local obstructions to the deformation theory of the associated residual Galois representations generically vanish.
Extending Sellers' result, Das et al. recently proved some congruence results for generalized overcubic partitions using theta functions and posed some related conjectures. In this paper, we provide a combinatorial proof of a result in…
In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving…
This paper has been withdrawn by the author due to a crucial error related with the consideration of regular points
In this paper we prove a conjecture that $D(4)$-quintuple does not exist using both classical and new methods. Also, we give a new version of the Rickert's theorem that can be applied on some $D(4)$-quadruples.