On Gorenstein Surfaces Dominated by P^2

In this paper we prove that a normal Gorenstein surface dominated by the projective plane P^2 is isomorphic to a quotient P^2/G, where G is a finite group of automorphisms of P^2 (except possibly for one surface V_8'). We can completely classify all such quotients. Some natural conjectures when the surface is not Gorenstein are also stated.Comment: Nagoya Mathematical Journal, to appea

On the Zariski-Lipman conjecture for normal algebraic surfaces

We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several classes of affine and projective surfaces.Comment: Final version; to appear in Jour. London Math. So

CT scan findings in patients of eclampsia

Background: Eclampsia is defined as the occurrence of one or more convulsions in association with raised blood pressure and proteinuria in a pregnant or puerperal woman, usually between 20 weeks’ gestation and the first 48 hours postpartum. Maternal mortality in India due to eclampsia is 2 to 30% and perinatal mortality is 30 to 50%. Abnormal findings on neuroimaging have been noted in as many as 80-90% of women with eclampsia. Most common lesions are seen in parieto-occipital lobes in the distribution of posterior cerebral arteries. This lesion occurs as a result of vasogenic oedema induced by endothelial damage and other changes contributing to pathophysiology of eclampsia. Objectives of present work were to study involvement of different areas of brain in eclampsia and to study maternal and fetal outcomes.Methods: This is a prospective study done over a period of 6 months the study population were chosen by random sampling who were eclampsia patients admitted trough emergency and also indoor patients who develop eclampsia after admission. Total 12 patients were analyzed. CT scan of brain performed after confinement of fetus and after stabilising the mother. Maternal and fetal outcomes were observed in these cases.Results: 58.33% (7cases) eclamptic mothers were primigravida and 41.66% (5 cases) were multigravida. Among them 16.66% (2 cases) had postpartum eclampsia while 83.33% (10 cases) had antepartum eclampsia. 75% mothers delivered by vaginal route and 25% mothers undergone LSCS. There were 14 births including 2 twin deliveries, out which 12 were live births and 2 Intra uterine deaths. On CT Scan- Brain stem edema was seen in 9 cases, infarction in 1case, hemorrhage in 1case and in 1 case CT was normal. Most common lobe involved is parietal (10 cases) followed by occipital (7 cases), frontal (4 cases), temporal (3 cases).Conclusions: Early recognition of the disorder and prompt management by control of blood pressure, removal of the offending medications or treatment of associated diseases is essential to prevent irreversible brain damage. CT scan of brain in eclampsia can provide useful intra cerebral information and should be done in cases with severe neurologic manifestations, if possible for every eclamptic mother