A new construction of Calabi–Yau manifolds: Generalized CICYs

We present a generalization of the complete intersection in products of projective space (CICY) construction of Calabi–Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility stems from the fact that they can be simply described in terms of a ‘configuration matrix’, a matrix of integers from which many of the details of the geometries can be easily extracted. The generalization we present is to allow negative integers in the configuration matrices which were previously taken to have positive semi-definite entries. This broadening of the complete intersection construction leads to a larger class of Calabi–Yau manifolds than that considered in previous work, which nevertheless enjoys much of the same degree of calculational control. These new Calabi–Yau manifolds are complete intersections in (not necessarily Fano) ambient spaces with an effective anticanonical class. We find examples with topology distinct from any that has appeared in the literature to date. The new manifolds thus obtained have many interesting features. For example, they can have smaller Hodge numbers than ordinary CICYs and lead to many examples with elliptic and K3-fibration structures relevant to F-theory and string dualities.

Ontogenie und Phylogenie der Belemnitenart Hibolites jaculoides SWINNERTON, 1937, aus dem Hauterivium (Unterkreide) von NW-Deutschland (Sarstedt) und NE England (Speeton)

The belemnite species Hibolites jaculoides Swinnerton, 1937 is redefined on the basis of a bed by bed collection of 2100 rostrums from the Upper Hauterivian (Cretaceous deposits of NW Germany and Yorkshire, England. According to the variate-statistical evaluation of the data gathered, definite phylotic changes are disdernible within the species. All characters measured indicate a definite tendency towards reduction in size. Large-sized, club-shaped specimens are typical for the stratigraphically older beds, delicate and slender-built forms dominate in the upper Upper Hauterivian. Comparison of the material from England and Germany yielded that three of the varieties described by Swinnerton are limited mainly to the lower Upper Hauterivian of England.