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.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data: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 $g_i$.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
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.
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Cite This Article
FINTUSHEL, R., STERN, R. (2022). The canonical class of a symplectic 4-manifold. Turkish Journal of Mathematics, Cilt: 25 - Sayı: 1, 137–145. https://ajindex.com/articles/608902
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