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1. Cremona Transformations. Let V = V 2n be the Segre product variety S n x S n ' of two /^-dimensional complex projective spaces. Then any Cremona transformation T of S n into S n ' (regarded as an irreducible algebraic system of oo" ordered pairs of points) is represented on V by an irreducible ^-dimensional subvariety H which satisfies (on V) the algebraic equivalencewhere S tiJ is a subvariety S f x S/ of V and mi, ...,m n _ 1 are positive integers. We call m u ..., w n _! the characters of T, noting that, numerically,Let (<£>) and OP) be the homaloidal systems of primals in S n and S n ' associated with T; and let <&' and *P J denote the free intersection varieties of sets of / independent generic primals of (

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There is no consensus on the optimal pCO2 levels in the newborn. We reviewed the effects of hypercapnia and hypocapnia and existing carbon dioxide thresholds in neonates. A systematic review was conducted in accordance with the PRISMA statement and MOOSE guidelines. Two hundred and ninety-nine studies were screened and 37 studies included. Covidence online software was employed to streamline relevant articles. Hypocapnia was associated with predominantly neurological side effects while hypercapnia was linked with neurological, respiratory and gastrointestinal outcomes and Retinpathy of prematurity (ROP). Permissive hypercapnia did not decrease periventricular leukomalacia (PVL), ROP, hydrocephalus or air leaks. As safe pCO2 ranges were not explicitly concluded in the studies chosen, it was indirectly extrapolated with reference to pCO2 levels that were found to increase the risk of neonatal disease. Although PaCO2 ranges were reported from 2.6 to 8.7 kPa (19.5–64.3 mmHg) in both term and preterm infants, there are little data on the safety of these ranges. For permissive hypercapnia, parameters described for bronchopulmonary dysplasia (BPD; PaCO2 6.0–7.3 kPa: 45.0–54.8 mmHg) and congenital diaphragmatic hernia (CDH; PaCO2 ≤ 8.7 kPa: ≤65.3 mmHg) were identified. Contradictory findings on the effectiveness of permissive hypercapnia highlight the need for further data on appropriate CO2 parameters and correlation with outcomes. Impact There is no consensus on the optimal pCO2 levels in the newborn. There is no consensus on the effectiveness of permissive hypercapnia in neonates. A safe range of pCO2 of 5–7 kPa was inferred following systematic review.