Related papers: Derived invariants arising from the Albanese map

This paper studies irregularity-type invariants of special C-pairs, or "geometric orbifolds" in the sense of Campana. Under mild assumptions on the singularities, we show that the augmented irregularity of a C-pair (X,D) is bounded by its…

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras A_i\in V, such that some finitely generated subalgebra S \subseteq A is dense in A under the inverse limit of the discrete topologies…

Higher extensions and higher central extensions, which are of importance to non-abelian homological algebra, are studied, and some fundamental properties are proven. As an application, a direct proof of the invariance of the higher Hopf…

Modified Derksen invariant HD*(X) of an affine variety X is a subalgebra in K[X] generated by kernels of all locally nilpotent derivations of K[X] with slices. If there is a locally nilpotent derivation of K[X] with a slice then X is a…

Let $X$ be a projective manifold. Let $Y_1,...,Y_{p+1}$ be $p+1$ ample hypersurfaces in complete intersection position on $X$, each defined by the global section of an ample Cartier divisor. We show in this note that for $i\le p+1$, the…

We study when a smooth variety $X$, embedded diagonally in its Cartesian square, is the zero scheme of a section of a vector bundle of rank $\dim(X)$ on $X\times X$. We call this the diagonal property (D). It was known that it holds for all…

We construct analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for links in the boundary of any smooth oriented 4-manifold. The main tools are skein lasagna modules based on equivariant and deformed versions of…

Let $A$ be an abelian variety over an algebraically closed field. We show that $A$ is the automorphism group scheme of some smooth projective variety if and only if $A$ has only finitely many automorphisms as an algebraic group. This…

Originally a technical tool, the derived category of coherent sheaves over an algebraic variety has become over the last twenty years an important invariant in the birational study of algebraic varieties. Problems of birational invariance…

In this report we give an intrinsic treatment of the results we developed in a previous work connecting the differential calculi on Hopf algebras to the Drinfeld double. In the first place we recover that bicovariant bimodules are in one to…

We show that isomorphisms of fundamental groups of elementary anabelian varieties -- varieties obtained as iterated fibrations of hyperbolic curves -- over sub-$p$-adic fields correspond bijectively to isomorphisms of varieties. Moreover,…

The notion of Lie $H$-pseudoalgebra is a higher-dimensional analogue of Lie conformal algebras. In this paper, we classify the equivalence classes of non-abelian extensions of a Lie $H$-pseudoalgebra $L$ by another Lie $H$-pseudoalgebra $M$…

In this article, we study the infinitemisal invariant of the relative higher Abel Jacobi map of a smooth open morphism. We give a generalization of a theorem of Voisin to open varieties and higher Chow groups and as a corollary a non…

We construct for every proper algebraic space over a ground field an Albanese map to a para-abelian variety, which is unique up to unique isomorphism. This holds in the absence of rational points or ample sheaves, and also for reducible or…

Assume $G$ is a polycyclic group and $\phi:G\to G$ an endomorphism. Let $G\ast_{\phi}$ be the ascending HNN extension of $G$ with respect to $\phi$; that is, $G\ast_{\phi}$ is given by the presentation $$G\ast_{\phi}= < G, t \ |\ t^{-1}gt =…

We introduce n-generated sheaves and n-motivic sheaves, describing completely for n = 0, 1 and proposing a conjecture for n > 1. We then obtain functors L\pi_0 and LAlb on DM_{eff}(k) deriving \pi_0 and Alb. The functor LAlb extends the one…

We construct, using geometric invariant theory, a quasi-projective Deligne-Mumford stack of stable graded algebras. We also construct a derived enhancement, which classifies twisted bundles of stable graded A-infinity-algebras. The tangent…

Let $B$ be the split extension of a finite dimensional algebra $C$ by a $C$-$C$-bimodule $E$. We define a morphism of associative graded algebras $\varphi^*:\HH^*(B)\rightarrow \HH^*(C)$ from the Hochschild cohomology of $B$ to that of $C$,…

We establish the Hodge conjecture for the top dimensional cohomology group with integer coefficients of any $q$-complete complex manifold $X$ with $q<\dim X$. This holds in particular for the complement $X=\mathbb{C}\mathbb{P}^n\setminus A$…

Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the…