Geometric invariant theory of syzygies, with applications to moduli spaces

We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.Comment: v1: 23 pages, submitted to the Proceedings of the Abel Symposium 2017, v2: final version, corrects a sign error and resulting divisor class calculations on the moduli space of K3 surfaces in Section 5, other minor changes, In: Christophersen J., Ranestad K. (eds) Geometry of Moduli. Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cha

Twelve Variants Polygenic Score for Low-Density Lipoprotein Cholesterol Distribution in a Large Cohort of Patients With Clinically Diagnosed Familial Hypercholesterolemia With or Without Causative Mutations

: Background A significant proportion of individuals clinically diagnosed with familial hypercholesterolemia (FH), but without any disease-causing mutation, are likely to have polygenic hypercholesterolemia. We evaluated the distribution of a polygenic risk score, consisting of 12 low-density lipoprotein cholesterol (LDL-C)-raising variants (polygenic LDL-C risk score), in subjects with a clinical diagnosis of FH. Methods and Results Within the Lipid Transport Disorders Italian Genetic Network (LIPIGEN) study, 875 patients who were FH-mutation positive (women, 54.75%; mean age, 42.47±15.00 years) and 644 patients who were FH-mutation negative (women, 54.21%; mean age, 49.73±13.54 years) were evaluated. Patients who were FH-mutation negative had lower mean levels of pretreatment LDL-C than patients who were FH-mutation positive (217.14±55.49 versus 270.52±68.59 mg/dL, P<0.0001). The mean value (±SD) of the polygenic LDL-C risk score was 1.00 (±0.18) in patients who were FH-mutation negative and 0.94 (±0.20) in patients who were FH-mutation positive (P<0.0001). In the receiver operating characteristic analysis, the area under the curve for recognizing subjects characterized by polygenic hypercholesterolemia was 0.59 (95% CI, 0.56-0.62), with sensitivity and specificity being 78% and 36%, respectively, at 0.905 as a cutoff value. Higher mean polygenic LDL-C risk score levels were observed among patients who were FH-mutation negative having pretreatment LDL-C levels in the range of 150 to 350 mg/dL (150-249 mg/dL: 1.01 versus 0.91, P<0.0001; 250-349 mg/dL: 1.02 versus 0.95, P=0.0001). A positive correlation between polygenic LDL-C risk score and pretreatment LDL-C levels was observed among patients with FH independently of the presence of causative mutations. Conclusions This analysis confirms the role of polymorphisms in modulating LDL-C levels, even in patients with genetically confirmed FH. More data are needed to support the use of the polygenic score in routine clinical practice

Refinement of the diagnostic approach for the identification of children and adolescents affected by familial hypercholesterolemia: Evidence from the LIPIGEN study

Background and aims: We aimed to describe the limitations of familiar hypercholesterolemia (FH) diagnosis in childhood based on the presence of the typical features of FH, such as physical sings of cholesterol accumulation and personal or family history of premature cardiovascular disease or hypercholesterolemia, comparing their prevalence in the adult and paediatric FH population, and to illustrate how additional information can lead to a more effective diagnosis of FH at a younger age.Methods: From the Italian LIPIGEN cohort, we selected 1188 (&gt;= 18 years) and 708 (&lt;18 years) genetically-confirmed heterozygous FH, with no missing personal FH features. The prevalence of personal and familial FH features was compared between the two groups. For a sub-group of the paediatric cohort (N = 374), data about premature coronary heart disease (CHD) in second-degree family members were also included in the evaluation.Results: The lower prevalence of typical FH features in children/adolescents vs adults was confirmed: the prevalence of tendon xanthoma was 2.1% vs 13.1%, and arcus cornealis was present in 1.6% vs 11.2% of the cohorts, respectively. No children presented clinical history of premature CHD or cerebral/peripheral vascular disease compared to 8.8% and 5.6% of adults, respectively. The prevalence of premature CHD in first-degree relatives was significantly higher in adults compared to children/adolescents (38.9% vs 19.7%). In the sub-cohort analysis, a premature CHD event in parents was reported in 63 out of 374 subjects (16.8%), but the percentage increased to 54.0% extending the evaluation also to second-degree relatives.Conclusions: In children, the typical FH features are clearly less informative than in adults. A more thorough data collection, adding information about second-degree relatives, could improve the diagnosis of FH at younger age

Familial hypercholesterolaemia in children and adolescents from 48 countries: a cross-sectional study

Background: Approximately 450 000 children are born with familial hypercholesterolaemia worldwide every year, yet only 2·1% of adults with familial hypercholesterolaemia were diagnosed before age 18 years via current diagnostic approaches, which are derived from observations in adults. We aimed to characterise children and adolescents with heterozygous familial hypercholesterolaemia (HeFH) and understand current approaches to the identification and management of familial hypercholesterolaemia to inform future public health strategies. Methods: For this cross-sectional study, we assessed children and adolescents younger than 18 years with a clinical or genetic diagnosis of HeFH at the time of entry into the Familial Hypercholesterolaemia Studies Collaboration (FHSC) registry between Oct 1, 2015, and Jan 31, 2021. Data in the registry were collected from 55 regional or national registries in 48 countries. Diagnoses relying on self-reported history of familial hypercholesterolaemia and suspected secondary hypercholesterolaemia were excluded from the registry; people with untreated LDL cholesterol (LDL-C) of at least 13·0 mmol/L were excluded from this study. Data were assessed overall and by WHO region, World Bank country income status, age, diagnostic criteria, and index-case status. The main outcome of this study was to assess current identification and management of children and adolescents with familial hypercholesterolaemia. Findings: Of 63 093 individuals in the FHSC registry, 11 848 (18·8%) were children or adolescents younger than 18 years with HeFH and were included in this study; 5756 (50·2%) of 11 476 included individuals were female and 5720 (49·8%) were male. Sex data were missing for 372 (3·1%) of 11 848 individuals. Median age at registry entry was 9·6 years (IQR 5·8-13·2). 10 099 (89·9%) of 11 235 included individuals had a final genetically confirmed diagnosis of familial hypercholesterolaemia and 1136 (10·1%) had a clinical diagnosis. Genetically confirmed diagnosis data or clinical diagnosis data were missing for 613 (5·2%) of 11 848 individuals. Genetic diagnosis was more common in children and adolescents from high-income countries (9427 [92·4%] of 10 202) than in children and adolescents from non-high-income countries (199 [48·0%] of 415). 3414 (31·6%) of 10 804 children or adolescents were index cases. Familial-hypercholesterolaemia-related physical signs, cardiovascular risk factors, and cardiovascular disease were uncommon, but were more common in non-high-income countries. 7557 (72·4%) of 10 428 included children or adolescents were not taking lipid-lowering medication (LLM) and had a median LDL-C of 5·00 mmol/L (IQR 4·05-6·08). Compared with genetic diagnosis, the use of unadapted clinical criteria intended for use in adults and reliant on more extreme phenotypes could result in 50-75% of children and adolescents with familial hypercholesterolaemia not being identified. Interpretation: Clinical characteristics observed in adults with familial hypercholesterolaemia are uncommon in children and adolescents with familial hypercholesterolaemia, hence detection in this age group relies on measurement of LDL-C and genetic confirmation. Where genetic testing is unavailable, increased availability and use of LDL-C measurements in the first few years of life could help reduce the current gap between prevalence and detection, enabling increased use of combination LLM to reach recommended LDL-C targets early in life

The Role of Registers in Increasing Knowledge and Improving Management of Children and Adolescents Affected by Familial Hypercholesterolemia: the LIPIGEN Pediatric Group

Pathology registers can be a useful tool to overcome obstacles in the identification and management of familial hypercholesterolemia since childhood. In 2018, the LIPIGEN pediatric group was constituted within the Italian LIPIGEN study to focus on FH subjects under 18 years. This work aimed at discussing its recent progress and early outcomes. Demographic, biochemical, and genetic baseline characteristics were collected, with an in-depth analysis of the genetic defects. The analysis was carried out on 1,602 children and adolescents (mean age at baseline 9.9 ± 4.0 years), and almost the whole cohort underwent the genetic test (93.3%). Overall, the untreated mean value of LDL-C was 220.0 ± 97.2 mg/dl, with an increasing gradient from subjects with a negative (N = 317; mean untreated LDL-C = 159.9 ± 47.7 mg/dl), inconclusive (N = 125; mean untreated LDL-C = 166.4 ± 56.5 mg/dl), or positive (N = 1,053; mean untreated LDL-C = 246.5 ± 102.1 mg/dl) genetic diagnosis of FH. In the latter group, the LDL-C values presented a great variability based on the number and the biological impact of involved causative variants. The LIPIGEN pediatric group represents one of the largest cohorts of children with FH, allowing the deepening of the characterization of their baseline and genetic features, providing the basis for further longitudinal investigations for complete details

Lipoprotein(a) and family history for cardiovascular disease in paediatric patients: A new frontier in cardiovascular risk stratification. Data from the LIPIGEN paediatric group

Background and aims: Little is known about the role of Lp(a) in the assessment of cardiovascular risk in the paediatric population. Trying to clarify the clinical relevance of Lp(a) in risk stratification, the aim of the study is to evaluate the association between Lp(a) plasma levels in children with familial hypercholesterolaemia (FH) and positive family history for premature cardiovascular disease (pCVD) in first-and second-degree relatives. Methods: 653 Caucasian children and adolescents (334 females and 319 males), aged 2-17 years, with diagnosis of FH from a paediatric cohort included in the LIPIGEN Network, were selected. We compared family history of pCVD, lipid and genetic profile in two groups based on Lp(a) levels below or above 30 mg/dL. To determine the independent predictors of pCVD, a multivariate logistic regression was used, with all clinical characteristics and blood measurements as predictors. Results: Subjects with Lp(a) > 30 mg/dl more frequently reported positive family history of pCVD compared to subjects with Lp(a) 30 mg/dl was an independent predictor of family history of pCVD. Comparing subjects with or without family history of pCVD, we reported significant differences for Lp(a) > 30 mg/dl (46.25% vs 17.65%, p 30 mg/dl where more likely to have a positive family history of pCVD. Lp(a) screening in children and adolescents with FH may enhance risk assessment and help identify those subjects, children and relatives, at increased pCVD risk