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Show allA note on quasi-polarized surfaces of general type whose sectional genus is equal to the irregularity
Abstract
Let $(X,L)$ be a quasi-polarized surface.
In our previous papers, we studied $(X,L)$ with $\kappa(X)=2$, $h^{0}(L)>0$ and $g(X,L)=h^{1}(\mathcal{O}_{X})$.
Here $g(X,L)$ denotes the sectional genus of $(X,L)$.
In this note, we give the classification of quasi-polarized surfaces $(X,L)$ of this type completely.
In our previous papers, we studied $(X,L)$ with $\kappa(X)=2$, $h^{0}(L)>0$ and $g(X,L)=h^{1}(\mathcal{O}_{X})$.
Here $g(X,L)$ denotes the sectional genus of $(X,L)$.
In this note, we give the classification of quasi-polarized surfaces $(X,L)$ of this type completely.
Keywords
Quasi-polarized surfaces; Sectional genus; irregularity