The paper is devoted to algebraic surfaces which can be obtained using a simple combinatorial procedure called the T-construction. The class of T-surfaces is sufficiently rich: for example, we construct T-surfaces of an arbitrary degree in RP³ which are M-surfaces. We also present a construction of T-surfaces in RP³ with dim H1 (RX; Z/2) > h1, 1(CX), where RX and CX are the real and the complex point sets of the surface.
1 Supported in part by the Norwegian Research Council for Science and the Humanities. It is a pleasure for this author to thank the Department of Mathematics of the University of Sofia for organizing the remarkable conference in Zlatograd during the period August 28-September 2, 1995. It is also a pleasure to thank the M.I.T. Department of Mathematics for its hospitality from January 1 to July 31, 1993, when this work was started. 2Supported in part by NSF grant 9400918-DMS.We introduce and study...
Let be a normal projective variety, and let be an ample Cartier divisor on . Suppose that is not the projective space. We prove that the twisted cotangent sheaf is generically nef with respect to the polarisation . As an application we prove a Kobayashi-Ochiai theorem for foliations: if is a foliation such that , then is at most the rank of .
The theory of slice-regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains of . When is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space .