Turkish Journal of Mathematics
DOI
-
Abstract
In this article we present examples of simply connected symplectic 4-manifolds X whose canonical classes are represented by complicated disjoint unions of symplectic submanifolds of X: Theorem. Given finite collections {g_i}, {m_i}, i=1,...,n, of positive integers, there is a minimal symplectic simply connected 4-manifold X whose canonical class is represented by a disjoint union of embedded symplectic surfaces K ~ S_{g_1,1} « ... « S_{g_1,m_1} « ... « S_{g_n,1} «... « S{g_n,m_n} where S_{g_i,j} is a surface of genus g_i. Furthermore, c_1^2(X) = c_h(X) - (2+ b) where b= S{i=1}^n m_i is the total number of connected components of the symplectic representative of the canonical class.
First Page
137
Last Page
146
Recommended Citation
FINTUSHEL, RONALD and STERN, RONALD (2001) "The canonical class of a symplectic four manifold," Turkish Journal of Mathematics: Vol. 25: No. 1, Article 8. Available at: https://journals.tubitak.gov.tr/math/vol25/iss1/8
