Related papers: Real rectifiable currents, holomorphic chains and …

We show that a $2k$-current $T$ on a complex manifold is a real holomorphic $k$-chain if and only if $T$ is locally real rectifiable, $d$-closed and has $\mathcal{H}^{2k}$-locally finite support. This result is applied to study homology…

We present some results concerning currents of integration on finite-dimensional analytic spaces in Hilbert spaces, using the setting of metric currents. In particular, we obtain the characterization of such currents as positive closed…

We study ergodic properties of compositions of holomorphic endomorphisms of the complex projective space chosen independently at random according to some probability distribution. Along the way, we construct positive closed currents which…

We consider $2$-dimensional integer rectifiable currents which are almost area minimizing and show that their tangent cones are everywhere unique. Our argument unifies a few uniqueness theorems of the same flavor, which are all obtained by…

We consider the class of integer rectifiable currents without boundary satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.

We propose a version of the Hodge conjecture in Bott-Chern cohomology and using results from characterizing real holomorphic chains by real rectifiable currents to provide a proof for this question. We define a Bott-Chern differential…

This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth bundle maps $\alpha : E \rightarrow F$ which, for smooth…

We prove that 2 dimensional Integral currents (i.e. integer multiplicity 2 dimensional rectifiable currents) which are almost complex cycles in an almost complex manifold admitting locally a compatible symplectic form are smooth surfaces…

Given a generically surjective holomorphic vector bundle morphism $f\colon E\to Q$, $E$ and $Q$ Hermitian bundles, we construct a current $R^f$ with values in $\Hom(Q,H)$, where $H$ is a certain derived bundle, and with support on the set…

We show that any semi-calibration of degree 2 is locally induced by a smooth almost complex structure. We provide some applications of this result in the regularity theory for semi-calibrated 2-currents

Affine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade's theorem is determined. The results are illustrated by an…

We study restriction of logarithmic Higgs bundles to the boundary divisor and we construct the corresponding nearby-cycles functor in positive characteristic. As applications we prove some strong semipositivity theorems for analogs of…

Generalized Hydrodynamics is a recent theory that describes the large scale transport properties of one dimensional integrable models. At the heart of this theory lies an exact quantum-classical correspondence, which states that the flows…

Let h : R $\rightarrow$ R+ be a lower semi-continuous subbadditive and even function such that h(0) = 0 and h($\theta$) $\ge$ $\alpha$|$\theta$| for some $\alpha$ > 0. The h-mass of a k-polyhedral chain P =$\sum$j $\theta$j$\sigma$j in R n…

Under assumptions about complete intersection, we prove that Coleff-Herrera type currents satisfy a robust calculus in the sense that natural regularizations of such currents can be multiplied to yield regularizations of the Coleff-Herrera…

The family of cycle completable graphs has several cryptomorphic descriptions, the equivalence of which has heretofore been proven by a laborious implication-cycle that detours through a motivating matrix completion problem. We give a…

We investigate the behavior of four coherent-like conditions in regular conductor squares. In particular, we find necessary and sufficient conditions in order that a pullback ring be a finite conductor ring, a coherent ring, a generalized…

Irreversibility of RG flows in two dimensions is shown using conserved vector currents. Out of a conserved vector current, a quantity decreasing along the RG flow is built up such that it is stationary at fixed points where it coincides…

This thesis is devoted to the study of algebraic cycles in projective hyper-K\"ahler manifolds and strict Calabi-Yau manifolds. It contributes to the understanding of Beauville's and Voisin's conjectures on the Chow rings of projective…

We prove that infinitely differentiable almost reducible quasi-periodic cocycles, under a Diophantine condition on the frequency vector, are almost reducible to a sequence of real constant cocycles with a sequence of real conjugations, up…