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

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

Campana points of bounded height on vector group compactifications

We initiate a systematic quantitative study of subsets of rational points that are integral with respect to a weighted boundary divisor on Fano orbifolds. We call the points in these sets Campana points. Earlier work of Campana and subsequently Abramovich shows that there are several reasonable competing definitions for Campana points. We use a version that delineates well different types of behaviour of points as the weights on the boundary divisor vary. This prompts a Manin-type conjecture on Fano orbifolds for sets of Campana points that satisfy a klt (Kawamata log terminal) condition. By importing work of Chambert-Loir and Tschinkel to our set-up, we prove a log version of Manin's conjecture for klt Campana points on equivariant compactifications of vector groups.Comment: 52 pages; minor revision, changes in the definition of Campana point

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

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

Genome-wide common and rare variant analysis provides novel insights into clozapine-associated neutropenia

The antipsychotic clozapine is uniquely effective in the management of schizophrenia; however, its use is limited by its potential to induce agranulocytosis. The causes of this, and of its precursor neutropenia, are largely unknown, although genetic factors have an important role. We sought risk alleles for clozapine-associated neutropenia in a sample of 66 cases and 5583 clozapine-treated controls, through a genome-wide association study (GWAS), imputed human leukocyte antigen (HLA) alleles, exome array and copy-number variation (CNV) analyses. We then combined associated variants in a meta-analysis with data from the Clozapine-Induced Agranulocytosis Consortium (up to 163 cases and 7970 controls). In the largest combined sample to date, we identified a novel association with rs149104283 (odds ratio (OR)=4.32, P=1.79 × 10−8), intronic to transcripts of SLCO1B3 and SLCO1B7, members of a family of hepatic transporter genes previously implicated in adverse drug reactions including simvastatin-induced myopathy and docetaxel-induced neutropenia. Exome array analysis identified gene-wide associations of uncommon non-synonymous variants within UBAP2 and STARD9. We additionally provide independent replication of a previously identified variant in HLA-DQB1 (OR=15.6, P=0.015, positive predictive value=35.1%). These results implicate biological pathways through which clozapine may act to cause this serious adverse effec

Copy number variation in bipolar disorder.

Large (>100 kb), rare (500 kb) CNVs in BD compared with SZ, most notably for deletions >1 Mb (P=9 × 10(-4))