SEMIREGULARITY VIA DERIVED DEFORMATION THEORY ...

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SEMIREGULARITY VIA DERIVED DEFORMATION THEORY J.P.PRIDHAM Abstract. We realise Buchweitz and Flenner's semiregularity map (and hence a fortiori Bloch's semiregularity map) as the tangent of a morphism of derived moduli functors. An immediate consequence is that it annihilates all obstructions (not just curvilinear ones) globally. Introduction In [Blo], Bloch defined a semiregularity map τ : H1(Z,NZ/X) → Hp−1(X,Ωp−1X ) for every local complete intersection Z of codimension p in a compact complex manifold X, and showed that curvilinear obstructions lie in the kernel of τ .

• construction above satisfies
• rham cohomology
• smooth
• chern character
• perfx
• simplicial semirings
• dg−algk
• 2 dr
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• functor
• map