Mathematical Research Letters

Volume 25 (2018)

Number 5

Tangent cones of Hermitian Yang–Mills connections with isolated singularities

Pages: 1429 – 1445



Adam Jacob (University of California at Davis)

Henrique Sá Earp (Unicamp, Universidade Estadual de Campinas, São Paulo, Brazil)

Thomas Walpuski (Michigan State University, East Lansing, Michigan, U.S.A.)


We give a simple direct proof of uniqueness of tangent cones for singular projectively Hermitian Yang–Mills connections on reflexive sheaves at isolated singularities modelled on a sum of $\mu$-stable holomorphic bundles over $\mathbf{P}^{n-1}$.

HSE and TW were partially supported by São Paulo State Research Council (FAPESP) grant 2015/50368-0 and the MIT–Brazil Lemann Seed Fund for Collaborative Projects. HSE is also funded by FAPESP grant 2014/24727-0 and Brazilian National Research Council (CNPq) grant PQ2 – 312390/2014-9.

Received 10 January 2017

Accepted 7 August 2017

Published 1 February 2019