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  "body": "\n## Summary\n\nAn Enriques surface is a smooth projective [[algebraic surface|KFTECAATKG]] with no holomorphic $1$-forms and no holomorphic $2$-forms.\nIts canonical divisor is not trivial, but twice it is trivial.\nOver $\\C$, every Enriques surface is the quotient of a [[K3 surface|Q3V566R6K2]] by an involution without fixed points.\nEnriques surfaces form one of the four classes of minimal surfaces of Kodaira dimension $0$.\nThey are non-rational surfaces with $q = p_g = 0$, which shows that Castelnuovo's rationality criterion needs the second plurigenus.\n\n## Explanations\n\n### L1 human\n\nTake a K3 surface with a symmetry of order two that moves every point.\nIdentifying each point with its image gives a new surface, half as big, which is an Enriques surface.\nIts canonical bundle is not trivial, but it becomes trivial after squaring it.\nSo an Enriques surface is a close relative of a K3 surface that has lost its holomorphic volume form.\n",
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