2019年10月9日
Smooth factorial affine surfaces of logarithmic Kodaira dimension zero with trivial units
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This paper considers the family $\mathscr{S}_0$ of smooth affine factorial<br />
surfaces of logarithmic Kodaira dimension 0 with trivial units over an<br />
algebraically closed field $k$. Our main result (Theorem 4.1) is that the<br />
number of isomorphism classes represented in $\mathscr{S}_0$ is at least<br />
countably infinite. This contradicts the earlier classification of Gurjar and<br />
Miyanishi [5] which asserted that $\mathscr{S}_0$ has at most two elements up<br />
to isomorphism when $k=\mathbb{C}$. Thus, the classification of surfaces in<br />
$\mathscr{S}_0$ for the field $\mathbb{C}$, long thought to have been settled,<br />
is an open problem.
surfaces of logarithmic Kodaira dimension 0 with trivial units over an<br />
algebraically closed field $k$. Our main result (Theorem 4.1) is that the<br />
number of isomorphism classes represented in $\mathscr{S}_0$ is at least<br />
countably infinite. This contradicts the earlier classification of Gurjar and<br />
Miyanishi [5] which asserted that $\mathscr{S}_0$ has at most two elements up<br />
to isomorphism when $k=\mathbb{C}$. Thus, the classification of surfaces in<br />
$\mathscr{S}_0$ for the field $\mathbb{C}$, long thought to have been settled,<br />
is an open problem.
- ID情報
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- arXiv ID : arXiv:1910.03494