ar X iv : m at h / 07 01 88 5 v 1 [ m at h . A G ] 3 0 Ja n 20 07 CONIC - CONNECTED MANIFOLDS

ar X iv : m at h / 06 01 74 3 v 1 [ m at h . SP ] 3 0 Ja n 20 06 DETERMINANTS OF ZEROTH ORDER OPERATORS

ar X iv : 0 90 1 . 32 11 v 1 [ m at h . A G ] 2 1 Ja n 20 09 COMPACT KÄHLER MANIFOLDS WITH ELLIPTIC HOMOTOPY TYPE

Simply connected compact Kähler manifolds of dimension up to three with elliptic homotopy type are characterized in terms of their Hodge diamonds. This is applied to classify the simply connected Kähler surfaces and Fano threefolds with elliptic homotopy type.

ar X iv : m at h / 05 01 55 6 v 1 [ m at h . D G ] 3 1 Ja n 20 05 Geometric Algebras

This is the first paper in a series of three where we develope a systematic approach to the geometric algebras of multivectors and ex-tensors. The series is followed by another one where those algebraic concepts are used in a novel presentation of the differential geometry of (smooth) manifolds of arbitrary global topology. The key calcu-lational tool in our program is the euclidean geometrical...

ar X iv : m at h / 04 01 12 6 v 1 [ m at h . N T ] 1 3 Ja n 20 04 THREE LECTURES ON THE RIEMANN ZETA - FUNCTION

ar X iv : m at h / 07 01 88 5 v 2 [ m at h . A G ] 9 M ar 2 00 8 CONIC - CONNECTED MANIFOLDS

We study a particular class of rationally connected manifolds, X ⊂ P , such that two general points x, x′ ∈ X may be joined by a conic contained in X. We prove that these manifolds are Fano, with b2 6 2. Moreover, a precise classification is obtained for b2 = 2. Complete intersections of high dimension with respect to their multi-degree provide examples for the case b2 = 1. The proof of the cla...