Related papers: Sur la conjecture des fibres de Seifert
We investigate Beauville's conjecture on the Chow ring of irreducible symplectic varieties. For special irreducible symplectic varieties we relate it to a conjecture on the existence of rational Lagrangian fibrations, which proves…
We establish a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of M\"{o}bius and divisor functions. Specifically, we prove that the ratios conjecture and an…
We prove the boundedness of complements modulo two conjectures: Borisov-Alexeev conjecture and effective adjunction for fibre spaces. We discuss the last conjecture and prove it in two particular cases.
We survey recent developments on the Restriction conjecture.
Proietti et al. (arXiv:1902.05080) reported on an experiment designed to settle, or at least to throw light upon, the paradox of Wigner's friend. Without questioning the rigor or ingenuity of the experimental protocol, I argue that its…
The present paper gives an example of a rigid spherical cone-manifold and that of a flexible one which are both Seifert fibred.
In this paper we prove the "Tiling implies Spectral" part of Fuglede's paper for the case of three intervals. Then we prove the "Spectral implies Tiling" part of the conjecture for the case of three equal intervals as also when the…
Several results about the union-closed sets conjecture are presented.
In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.
We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration, using elementary geometry--indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives.
In this paper we review the hole argument for the space-time points and elementary particles and generalize the hole argument to include all geometric object fields and diffeomorphisms; and, by application of forgetful functors to abstract…
Given a fibre space $X/S$ with the generic geometric fibre of Kodaira dimension $\geq 0$, we shall construct a variety $Y$ ramified over $X$ along such a horizontal hyperplane with respect to $X/S$ that Koll\'ar and Kawamata had proved…
I give a simplified proof of one of the main results in the recent preprint arXiv:1311.5858 by X. Luo and K. Zuo. Furthermore, I discuss the relation with the Coleman-Oort conjecture on special curves in the Torelli locus.
In this note we give a counterexample to a conjecture proposed by Ciliberto about special linear systems of P^n through multiple base points.
We fix some gaps of a proof of Xiao's conjecture on canonically fibered surfaces of relative genus 5 by the second author. Our argument simplifies the original proof and gives a much better bound on the geometric genus of the surface. Also…
A conjecture of Kato says that the monodromy operator on the cohomology of a semi-stable degeneration of projective varieties is represented by an algebraic cycle on the special fiber of a normal crossing model of the fiber product…
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
These notes give an exposition of Deligne's theorem on the existense of super fiber functor.
The second author studied arithmetic properties of a class of sequences that generalize the sequence of derangements. The aim of the following paper is to disprove two conjectures stated in \cite{miska}. The first conjecture regards the set…
We prove the Strengthened Hanna Neumann Conjecture. We give a more direct cohomological interpretation of the conjecture in terms of "typical" covering maps, and use graph Galois theory to "symmetrize" the conjecture. The conjecture is then…