On the canonical degrees of curves in varieties of general type

A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general type is bounded from above by some expression $a\chi(C)+b$, where $a$ and $b$ are positive constants, with the possible exceptions corresponding to curves lying in a strict closed subset (depending on $a$ and $b$). A theorem of Miyaoka proves this for smooth curves in minimal surfaces, with $a>3/2$. A conjecture of Vojta claims in essence that any constant $a>1$ is possible provided one restricts oneself to curves of bounded gonality. We show by explicit examples coming from the theory of Shimura varieties that in general, the constant $a$ has to be at least equal to the dimension of the ambient variety. We also prove the desired inequality in the case of compact Shimura varieties.Comment: 10 pages, to appear in Geometric and Functional Analysi

Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: The minimal dimension of a canonical measure)

In this paper, we formulate the geometric Bogomolov conjecture for abelian varieties, and give some partial answers to it. In fact, we insist in a main theorem that under some degeneracy condition, a closed subvariety of an abelian variety does not have a dense subset of small points if it is a non-special subvariety. The key of the proof is the study of the minimal dimension of the components of a canonical measure on the tropicalization of the closed subvariety. Then we can apply the tropical version of equidistribution theory due to Gubler. This article includes an appendix by Walter Gubler. He shows that the minimal dimension of the components of a canonical measure is equal to the dimension of the abelian part of the subvariety. We can apply this result to make a further contribution to the geometric Bogomolov conjecture.Comment: 30 page

Clonal Hematopoiesis and Blood-Cancer Risk Inferred from Blood DNA Sequence

Background Cancers arise from multiple acquired mutations, which presumably occur over many years. Early stages in cancer development might be present years before cancers become clinically apparent. Methods We analyzed data from whole-exome sequencing of DNA in peripheral-blood cells from 12,380 persons, unselected for cancer or hematologic phenotypes. We identified somatic mutations on the basis of unusual allelic fractions. We used data from Swedish national patient registers to follow health outcomes for 2 to 7 years after DNA sampling. Results Clonal hematopoiesis with somatic mutations was observed in 10% of persons older than 65 years of age but in only 1% of those younger than 50 years of age. Detectable clonal expansions most frequently involved somatic mutations in three genes (DNMT3A, ASXL1, and TET2) that have previously been implicated in hematologic cancers. Clonal hematopoiesis was a strong risk factor for subsequent hematologic cancer (hazard ratio, 12.9; 95% confidence interval, 5.8 to 28.7). Approximately 42% of hematologic cancers in this cohort arose in persons who had clonality at the time of DNA sampling, more than 6 months before a first diagnosis of cancer. Analysis of bone marrow–biopsy specimens obtained from two patients at the time of diagnosis of acute myeloid leukemia revealed that their cancers arose from the earlier clones. Conclusions Clonal hematopoiesis with somatic mutations is readily detected by means of DNA sequencing, is increasingly common as people age, and is associated with increased risks of hematologic cancer and death. A subset of the genes that are mutated in patients with myeloid cancers is frequently mutated in apparently healthy persons; these mutations may represent characteristic early events in the development of hematologic cancers. (Funded by the National Human Genome Research Institute and others.)National Human Genome Research Institute (U.S.) (Grant U54 HG003067)National Human Genome Research Institute (U.S.) (Grant R01 HG006855)Stanley Center for Psychiatric ResearchAlexander and Margaret Stewart TrustNational Institute of Mental Health (U.S.) (Grant R01 MH 077139)National Institute of Mental Health (U.S.) (Grant RC2 MH089905)Sylvan C. Herman Foundatio

Genome-wide association study identifies 30 loci associated with bipolar disorder.

Bipolar disorder is a highly heritable psychiatric disorder. We performed a genome-wide association study (GWAS) including 20,352 cases and 31,358 controls of European descent, with follow-up analysis of 822 variants with P < 1 × 10-4 in an additional 9,412 cases and 137,760 controls. Eight of the 19 variants that were genome-wide significant (P < 5 × 10-8) in the discovery GWAS were not genome-wide significant in the combined analysis, consistent with small effect sizes and limited power but also with genetic heterogeneity. In the combined analysis, 30 loci were genome-wide significant, including 20 newly identified loci. The significant loci contain genes encoding ion channels, neurotransmitter transporters and synaptic components. Pathway analysis revealed nine significantly enriched gene sets, including regulation of insulin secretion and endocannabinoid signaling. Bipolar I disorder is strongly genetically correlated with schizophrenia, driven by psychosis, whereas bipolar II disorder is more strongly correlated with major depressive disorder. These findings address key clinical questions and provide potential biological mechanisms for bipolar disorder

De novo CNV analysis implicates specific abnormalities of postsynaptic signalling complexes in the pathogenesis of schizophrenia

A small number of rare, recurrent genomic copy number variants (CNVs) are known to substantially increase susceptibility to schizophrenia. As a consequence of the low fecundity in people with schizophrenia and other neurodevelopmental phenotypes to which these CNVs contribute, CNVs with large effects on risk are likely to be rapidly removed from the population by natural selection. Accordingly, such CNVs must frequently occur as recurrent de novo mutations. In a sample of 662 schizophrenia proband–parent trios, we found that rare de novo CNV mutations were significantly more frequent in cases (5.1% all cases, 5.5% family history negative) compared with 2.2% among 2623 controls, confirming the involvement of de novo CNVs in the pathogenesis of schizophrenia. Eight de novo CNVs occurred at four known schizophrenia loci (3q29, 15q11.2, 15q13.3 and 16p11.2). De novo CNVs of known pathogenic significance in other genomic disorders were also observed, including deletion at the TAR (thrombocytopenia absent radius) region on 1q21.1 and duplication at the WBS (Williams–Beuren syndrome) region at 7q11.23. Multiple de novos spanned genes encoding members of the DLG (discs large) family of membrane-associated guanylate kinases (MAGUKs) that are components of the postsynaptic density (PSD). Two de novos also affected EHMT1, a histone methyl transferase known to directly regulate DLG family members. Using a systems biology approach and merging novel CNV and proteomics data sets, systematic analysis of synaptic protein complexes showed that, compared with control CNVs, case de novos were significantly enriched for the PSD proteome (P=1.72 × 10−6). This was largely explained by enrichment for members of the N-methyl-D-aspartate receptor (NMDAR) (P=4.24 × 10−6) and neuronal activity-regulated cytoskeleton-associated protein (ARC) (P=3.78 × 10−8) postsynaptic signalling complexes. In an analysis of 18 492 subjects (7907 cases and 10 585 controls), case CNVs were enriched for members of the NMDAR complex (P=0.0015) but not ARC (P=0.14). Our data indicate that defects in NMDAR postsynaptic signalling and, possibly, ARC complexes, which are known to be important in synaptic plasticity and cognition, play a significant role in the pathogenesis of schizophrenia

Evidence that duplications of 22q11.2 protect against schizophrenia.

A number of large, rare copy number variants (CNVs) are deleterious for neurodevelopmental disorders, but large, rare, protective CNVs have not been reported for such phenotypes. Here we show in a CNV analysis of 47 005 individuals, the largest CNV analysis of schizophrenia to date, that large duplications (1.5-3.0 Mb) at 22q11.2--the reciprocal of the well-known, risk-inducing deletion of this locus--are substantially less common in schizophrenia cases than in the general population (0.014% vs 0.085%, OR=0.17, P=0.00086). 22q11.2 duplications represent the first putative protective mutation for schizophrenia