Instantons and curves on class VII surfaces

By A. Teleman. 2007

49 citations recorded by the source corpus.

We develop a general strategy, based on gauge theoretical methods, to prove existence of curves on class VII surfaces. We prove that, for $b_2=2$, every minimal class VII surface has a cycle of rational curves hence, by a result of Nakamura, is a global deformation of a one parameter family of blown up primary Hopf surfaces. The case $b_2=1$ has been solved in a previous article. The fundamental object intervening in our strategy is the moduli space ${\mathcal M}^{\pst}(0,{\mathcal K})$ of polystable bundles ${\mathcal E}$ with $c_2({\mathcal E})=0$, $\det({\mathcal E})={\mathcal K}$. For large $b_2$ the geometry of this moduli space becomes very complicated. The case $b_2=2$ treated here in detail requires new ideas and difficult techniques of both complex geometric and gauge theoretical nature.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a31b48484872f6d5060b1c0b539bb386b32d040b

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In Applied Mathematics

  1. Valentino Tosatti
  2. B. Weinkove
  3. Xiaokui Yang
  4. G'abor Sz'ekelyhidi
  5. Duong H. Phong
  6. Dat T. To
  7. M. Gill
  8. Jianchun Chu

In Geometry and Topology

  1. Valentino Tosatti
  2. B. Weinkove
  3. Xiaokui Yang
  4. G'abor Sz'ekelyhidi
  5. Duong H. Phong
  6. Dat T. To
  7. M. Gill
  8. Jianchun Chu

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