Anti-self-dual blowups

Vsevolod Shevchishin; Gleb Smirnov

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arXiv · 2308.03090

Anti-self-dual blowups

Vsevolod Shevchishin·Gleb Smirnov

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Abstract

Let $X$ be a closed, oriented four-manifold containing an embedded sphere with self-intersection number $(-1)$. Suppose that $b_2^+(X) \leq 3$. We show that there exists a Riemannian metric on $X$ such that the cohomology class dual to this sphere is represented by an anti-self-dual harmonic form. Furthermore, such a metric can be constructed even when there are multiple disjoint embedded $(-1)$-spheres.

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BibTeX RIS

Vsevolod Shevchishin, Gleb Smirnov. 2023-08-06. Anti-self-dual blowups. https://arxiv.org/abs/2308.03090

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