Smooth surfaces have finitely generated canonical rings and projective canonical models. For normal surfaces, however, the graded ring of multicanonical sections is possibly nonnoetherian, such that the corresponding homogeneous spectrum is noncompact. I construct a canonical compactification by adding finitely many non-Q-Gorenstein points at infinity, provided that each Weil divisor is numeric...

This book is about elliptic curves and modular functions, two topics that are intimately related in both accidental and essential ways. As emphasized by André Weil in his magisterial historical introduction to contemporary number theory [W], the arithmetic study of elliptic curves is, in spite of the clear reference to the integral calculus in the adjective elliptic, in many respects antecedent...

We reduce the vectorial binary Darboux transformation for the Manin-Radul supersymmetric KdV system in such a way that it preserves the Manin-Radul-Mathieu supersymmetric KdV equation reduction. Expressions in terms of bosonic Pfaffians are provided for transformed solutions and wave functions. We also consider the implications of these results for the supersymmetric sine-Gordon equation. On le...

We prove that the elliptic surface y 2 = x 3 + 2(t 8 + 14t 4 + 1)x + 4t 2 (t 8 + 6t 4 + 1) has geometric Mordell-Weil rank 15. This completes a list of Kuwata, who gave explicit examples of elliptic K3-surfaces with geometric Mordell

Leptospiral meningitis, which is an important feature of anicteric leptospirosis, is generally underdiagnosed. Serological tests are not very useful in diagnosis of leptospiral meningitis. Early detection by molecular tests such as PCR and prompt institution of therapy would be life-saving.

results; out of 634 patients, 61 subjects (9.62%) had significant complications including: acute renal failure, alveolar hemorrhage, ards, clotting disorders, pancreatitis, gastrointestinal bleeding and intracranial bleeding; age, jaundice, renal and pulmonary involvement (oliguria and anuria), hypotension, leukocytosis, thrombocytopenia, hyponatremia, elevated bilirubin, alanine aminotransfera...

One of the main purpose of this paper is to compare those well-known canonical and complete metrics on the Teichmüller and the moduli spaces of Riemann surfaces. We use as bridge two new metrics, the Ricci metric and the perturbed Ricci metric. We will prove that these metrics are equivalent to those classical complete metrics. For this purpose we study in detail the asymptotic behaviors and th...

We shall show that the Picard number of the generic fiber of an abelian fibered hyperkähler manifold over the projective space is always one. We then give a few applications for the Mordell-Weil group. In particular, by deforming O’Grady’s 10dimensional manifold, we construct an abelian fibered hyperkähler manifold of MordellWeil rank 20, which is the maximum possible among all known ones.