Infinitesimal automorphisms of L-valued G-Higgs bundles are computed, proving the stable moduli stack is Deligne-Mumford for semisimple G and yielding a symmetric perfect obstruction theory on surfaces when L = K_X.
Manolache,Virtual pull-backs, Journal of Algebraic Geometry.21(2)(2012), 201–245
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Infinitesimal automorphisms and obstruction theory on the moduli of $L$-valued $G$-Higgs bundles
Infinitesimal automorphisms of L-valued G-Higgs bundles are computed, proving the stable moduli stack is Deligne-Mumford for semisimple G and yielding a symmetric perfect obstruction theory on surfaces when L = K_X.