A toric blow-up method computes the integral cohomology of quotients by cyclic prime-order groups and yields new Beauville-Bogomolov lattices for K3[m]-type quotients by order 5 and 7 symmetries.
Menet, On the integral cohomology of quotients of complex manifold s, Journal de Mathé- matiques pures et appliquées, 119 (2018), no.9, 280-325
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Integral cohomology of quotients via toric geometry
A toric blow-up method computes the integral cohomology of quotients by cyclic prime-order groups and yields new Beauville-Bogomolov lattices for K3[m]-type quotients by order 5 and 7 symmetries.