## Prof. Dr. Hartmut Weiss

### Project leader

Christian-Albrechts-Universität zu Kiel

E-mail: weiss(at)math.uni-kiel.de

Telephone: +49 431 880-2790

Homepage: https://www.math.uni-kiel.de/geometrie/d...

## Publications within SPP2026

We study the asymptotics of the natural \(L^2\) metric on the Hitchin moduli space with group \(G=SU(2)\). Our main result, which addresses a detailed conjectural picture made by Gaiotto, Neitzke and Moore, is that on the regular part of the Hitchin system, this metric is well-approximated by the semiflat metric. We prove that the asymptotic rate of convergence for gauged tangent vectors to the moduli space has a precise polynomial expansion, and hence that the the difference between the two sets of metric coefficients in a certain natural coordinate system also has polynomial decay. Very recent work by Dumas and Neitzke indicates that the convergence rate for the metric is exponential, at least in certain directions.

**Related project(s):****32**Asymptotic geometry of the Higgs bundle moduli space

We prove a gluing theorem for solutions \((A_0, \Phi_0)\) of Hitchin's self-duality equations with logarithmic singularities on a rank-\(2\) vector bundle over a noded Riemann surface \( \Sigma\) representing a boundary point of Teichmüller moduli space. We show that every nearby smooth Riemann surface \( \Sigma_1\) carries a smooth solution \((A_1, \Phi_1)\) of the self-duality equations, which may be viewed as a desingularization of \((A_0, \Phi_0)\).

Journal | Adv. Math. |

Publisher | Elsevier |

Volume | 322 |

Pages | 637-681 |

Link to preprint version | |

Link to published version |

**Related project(s):****32**Asymptotic geometry of the Higgs bundle moduli space

We associate to each stable Higgs pair \((A_0,\Phi_0)\) on a compact Riemann surface *X* a singular limiting configuration \((A_\infty,\Phi_\infty)\), assuming that \(\det\Phi\) has only simple zeroes. We then prove a desingularization theorem by constructing a family of solutions \((A_t,\Phi_t) \) to Hitchin's equations which converge to this limiting configuration as \(t\to\infty\). This provides a new proof, via gluing methods, for elements in the ends of the Higgs bundle moduli space and identifies a dense open subset of the boundary of the compactification of this moduli space.

Journal | Duke Math. J. |

Publisher | Duke University Press |

Volume | 165 |

Pages | 2227-2271 |

Link to preprint version | |

Link to published version |

**Related project(s):****32**Asymptotic geometry of the Higgs bundle moduli space