Let σ be an anti-holomorphic involution on an almost complex four manifold X,a necessary and sufficient condition is given to determine weather X/σ admits an almost complex structure.
There are three key ingredients in the study of the minimal genus problem for rational surfaces CP2#nCP2: the generalized adjunction formula, the action of the orthogonal group of the Lorentz space and the geometric construction. In this paper, we prove the uniqueness of the standard form (see Definition 1.1 and Theorem 1.1) of a 2-dimensional homology class under the action of the subgroup of the Lorentz orthogonal group that is realized by the diffeomorphisms of CP2#nCP2.Using the geometric construction, we determine the minimal genera of some classes (see Theorem 1.2).
ZHAO Xu’an,GAO Hongzhu & QIU Huaidong LMAM,School of Mathematics Science, Beijing Normal University, Beijing 100875, China
