Equidistribution of zeros of holomorphic sections in the non compact setting

We consider N-tensor powers of a positive Hermitian line bundle L over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed with respect to the natural measure coming from the curvature of L, as N tends to infinity. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to the principal congruence subgroups of SL2(Z) and to the hyperbolic measure, the higher dimensional case of arithmetic quotients and the case of orthogonal polynomials with weights at infinity. We also give estimates for the speed of convergence of the currents of integration on the zero-divisors.Comment: 25 pages; v.2 is a final update to agree with the published pape

On Proper Polynomial Maps of C2.\mathbb{C}^2.

Two proper polynomial maps $f_1, f_2 \colon \mathbb{C}^2 \longrightarrow \mathbb{C}^2$ are said to be \emph{equivalent} if there exist $\Phi_1, \Phi_2 \in \textrm{Aut}(\mathbb{C}^2)$ such that $f_2=\Phi_2 \circ f_1 \circ \Phi_1$. We investigate proper polynomial maps of arbitrary topological degree $d \geq 2$ up to equivalence. Under the further assumption that the maps are Galois coverings we also provide the complete description of equivalence classes. This widely extends previous results obtained by Lamy in the case $d=2$.Comment: 15 pages. Final version, to appear in Journal of Geometric Analysi

Invariant elliptic curves as attractors in the projective plane

Let f be a rational self-map of P^2 which leaves invariant an elliptic curve C with strictly negative transverse Lyapunov exponent. We show that C is an attractor, i.e. it possesses a dense orbit and its basin is of strictly positive measure

Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)

[no abstract available

Mapping and characterization of structural variation in 17,795 human genomes

A key goal of whole-genome sequencing for studies of human genetics is to interrogate all forms of variation, including single-nucleotide variants, small insertion or deletion (indel) variants and structural variants. However, tools and resources for the study of structural variants have lagged behind those for smaller variants. Here we used a scalable pipeline1 to map and characterize structural variants in 17,795 deeply sequenced human genomes. We publicly release site-frequency data to create the largest, to our knowledge, whole-genome-sequencing-based structural variant resource so far. On average, individuals carry 2.9 rare structural variants that alter coding regions; these variants affect the dosage or structure of 4.2 genes and account for 4.0–11.2% of rare high-impact coding alleles. Using a computational model, we estimate that structural variants account for 17.2% of rare alleles genome-wide, with predicted deleterious effects that are equivalent to loss-of-function coding alleles; approximately 90% of such structural variants are noncoding deletions (mean 19.1 per genome). We report 158,991 ultra-rare structural variants and show that 2% of individuals carry ultra-rare megabase-scale structural variants, nearly half of which are balanced or complex rearrangements. Finally, we infer the dosage sensitivity of genes and noncoding elements, and reveal trends that relate to element class and conservation. This work will help to guide the analysis and interpretation of structural variants in the era of whole-genome sequencing

GW190814: gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object

We report the observation of a compact binary coalescence involving a 22.2–24.3 Me black hole and a compact object with a mass of 2.50–2.67 Me (all measurements quoted at the 90% credible level). The gravitational-wave signal, GW190814, was observed during LIGO’s and Virgo’s third observing run on 2019 August 14 at 21:10:39 UTC and has a signal-to-noise ratio of 25 in the three-detector network. The source was localized to 18.5 deg2 at a distance of - + 241 45 41 Mpc; no electromagnetic counterpart has been confirmed to date. The source has the most unequal mass ratio yet measured with gravitational waves, - + 0.112 0.009 0.008, and its secondary component is either the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system. The dimensionless spin of the primary black hole is tightly constrained to �0.07. Tests of general relativity reveal no measurable deviations from the theory, and its prediction of higher-multipole emission is confirmed at high confidence. We estimate a merger rate density of 1–23 Gpc−3 yr−1 for the new class of binary coalescence sources that GW190814 represents. Astrophysical models predict that binaries with mass ratios similar to this event can form through several channels, but are unlikely to have formed in globular clusters. However, the combination of mass ratio, component masses, and the inferred merger rate for this event challenges all current models of the formation and mass distribution of compact-object binaries

Open data from the third observing run of LIGO, Virgo, KAGRA, and GEO

The global network of gravitational-wave observatories now includes five detectors, namely LIGO Hanford, LIGO Livingston, Virgo, KAGRA, and GEO 600. These detectors collected data during their third observing run, O3, composed of three phases: O3a starting in 2019 April and lasting six months, O3b starting in 2019 November and lasting five months, and O3GK starting in 2020 April and lasting two weeks. In this paper we describe these data and various other science products that can be freely accessed through the Gravitational Wave Open Science Center at https://gwosc.org. The main data set, consisting of the gravitational-wave strain time series that contains the astrophysical signals, is released together with supporting data useful for their analysis and documentation, tutorials, as well as analysis software packages