Related papers: Some remarks on modified diagonals
O'Grady studied recently $m$-th modified diagonals for a smooth projective variety, generalizing the Gross-Schoen modified small diagonal. These cycles $\Gamma^m(X,a)$ depend on a choice of reference point $a\in X$ (or more generally a…
Let X be an abelian variety of dimension g. In a recent preprint O'Grady defines modified diagonal classes \Gamma^m on X^m and he conjectures that the class of \Gamma^m in the Chow ring of X^m is torsion for m \geq 2g+1. We prove a…
We prove vanishing results for the modified diagonal cycles in the Chow groups of the triple products of Shimura curves and their motivic direct summands. In particular we find examples of curves with trivial automorphism groups and…
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
We discuss class of doubled geometry models with diagonal metrics. Based on the analysis of known examples we formulate a hypothesis that supports treating them as modified bimetric gravity theories. Certain steps towards the generic case…
In this paper, we prove the geometric Bombieri-Lang conjecture for projective varieties which have finite morphisms to abelian varieties of trivial traces over function fields of characteristic 0. The proof is based on the idea of…
We prove the multiple cover formula conjecture for abelian surfaces for a large class of insertions, including all stationary invariants. The proof uses the reduced degeneration formula expressing the invariants in terms of the correlated…
A "reduced" differential geometry adapted to the presence of abelian isometries is constructed.Classical T-duality diagonalizes in this setting, allowing us to get conveniently the transformation of the relevant geometrical objects such as…
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…
We prove that small deformations of a projective variety of general type are also projective varieties of general type, with the same plurigenera. Version 2: small changes in first half. Improved version of the second half is now a separate…
We study restricted homomorphism dualities in the context of classes with bounded expansion. This presents a generalization of restricted dualities obtained earlier for bounded degree graphs and also for proper minor closed classes. This is…
In this mostly expository note, we explain a proof of Tate's two conjectures [Tat65] for algebraic cycles of arbitrary codimension on certain products of elliptic curves and abelian surfaces over number fields.
We generalise recent results about quasi-Cartan, Cartan and diagonal subalgebras by introducing graded versions. We show that there is a correspondence between graded algebraic quasi-Cartan/ Cartan/ diagonal pairs and certain graded twisted…
It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL_2-type over \Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism…
We prove some general results on syzygies of smooth projective varieties with numerically trivial canonical line bundle. This allows to confirm several cases of Mukai's syzygies conjecture for finite quotients of abelian varieties in any…
We construct geometric examples of N-differential graded algebras such as the algebra of differential forms of depth $N$ on an affine manifold, and $N$-flat covariant derivatives.
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
The algebraic degeneracy of holomorphic curves in a semi-Abelian variety omitting a divisor is proved (Lang's conjecture generalized to semi-Abelian varieties) by making use of the {\it jet-projection method} and the logarithmic Wronskian…