Related papers: On the Beauville conjecture

This paper is a step in our program for proving the Piece-Birkhoff Conjecture for regular rings of any dimension (this would contain, in particular, the classical Pierce-Birkhoff conjecture which deals with polynomial rings over a real…

Our first goal in this note is to explain that a weak form of Perrin-Riou's conjecture on the non-triviality of Beilinson-Kato classes follows as an easy consequence of the Iwasawa main conjectures, and deduce its refined versions in the…

Let F be a polarized irreducible holomorphic symplectic fourfold, deformation equivalent to the Hilbert scheme parametrizing length-two zero-dimensional subschemes of a K3 surface. The homology group H^2(F,Z) is equipped with an integral…

We generalize Voisin's theorem on deformations of pairs of a symplectic manifold and a Lagrangian submanifold to the case of Lagrangian normal crossing subvarieties. Partial results are obtained for arbitrary Lagrangian subvarieties. We…

Assuming the Morrison-Kawamata cone conjecture for the generic fiber of a Calabi-Yau fibration and the abundance conjecture, we show (1) the finiteness of minimal models, (2) the existence of a weak rational polyhedral fundamental domain…

We introduce how to pushforward shifted symplectic fibrations along base changes. This is achieved by considering symplectic forms that are closed in a stronger sense. Examples include: symplectic zero loci and symplectic quotients.…

The Chow rank of a form is the length of its smallest decomposition into a sum of products of linear forms. For a generic form, this corresponds to finding the smallest secant variety of the Chow variety which fills the ambient space. We…

In the studies on the modularity conjecture for rigid Calabi-Yau threefolds several examples with the unique level 8 cusp form were constructed. According to the Tate Conjecture correspondences inducing isomorphisms on the middle…

Let X be a smooth, complete, geometrically connected curve over a field of characteristic p. The geometric Langlands conjecture states that to each irreducible rank n local system E on X one can attach a perverse sheaf on the moduli stack…

We adapt Wei Zhang's proof of Kolyvagin's conjecture for modular abelian varieties over $\mathbb{Q}$ to rely on the BDP main conjecture instead of on the cyclotomic main conjecture. The main ingredient is a reduction to a case that is…

Between 1994 and 1998, the work of M. Brou\'e, G. Malle, and R. Rouquier generalized in a natural way the definition of the Hecke algebra associated to a finite Coxeter group, for the case of an arbitrary complex reflection group.…

We study the Picard rank of smooth toric Fano varieties possessing families of minimal rational curves of given degree. We discuss variants of a conjecture of Chen-Fu-Hwang and prove a version of their statement that recovers the original…

We prove an absolute Chow-Kuenneth decomposition for the motive of universal families A of abelian varieties over some compact Shimura surface. We furthermore prove the Hodge conjecture for general fibres of A, extending results of Ribet.

We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of…

The main theme of this paper is the introduction of a new type of polarizations, suited for some open symplectic manifolds, and their applications. These applications include symplectic embedding results that answer a question by…

We study the relative cone conjecture for families of $K$-trivial varieties with vanishing irregularity. As an application we prove that the relative movable and the relative nef cone conjectures hold for fibrations in projective IHS…

We give examples over arbitrary fields of rings of invariants that are not finitely generated. The group involved can be as small as three copies of the additive group, as in Mukai's examples over the complex numbers. The failure of finite…

We give a short proof of the log-concavity of the coefficients of the reduced characteristic polynomial of a matroid. The proof uses an extension of the theory of Lorentzian polynomials to convex cones, and reproves the Hodge-Riemann…

We study the relations between the finite generation of Cox ring, the rationality of Euler-Chow series and Poincar\'e series and Zariski's conjecture on dimensions of linear systems. We prove that if the Cox ring of a smooth projective…

This article is about hyperk\"ahler fourfolds $X$ admitting a non-symplectic involution $\iota$. The Bloch-Beilinson conjectures predict the way $\iota$ should act on certain pieces of the Chow groups of $X$. The main result is a…