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arXiv · 2111.15201

Upper bounds for virtual dimensions of Seiberg-Witten moduli spaces

Tsuyoshi Kato·Daisuke Kishimoto·Nobuhiro Nakamura·Kouichi Yasui
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Abstract

Given a closed four-manifold with $b_1=0$ and a prime number $p$, we prove that for any mod $p^r$ basic class, the virtual dimension of the Seiberg-Witten moduli space is bounded above by $2r(p-1)-2$ under some conditions on $r$ and $b_2^+$. As an application, we obtain adjunction inequalities for embedded surfaces with negative self-intersection number.

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Tsuyoshi Kato, Daisuke Kishimoto, Nobuhiro Nakamura, Kouichi Yasui. 2021-11-30. Upper bounds for virtual dimensions of Seiberg-Witten moduli spaces. https://arxiv.org/abs/2111.15201

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