Zero map between obstruction spaces: subvarieties versus cycles

2017/08/09 by Sen Yang, Yang, Sen
Mathematics · Computer Science · Engineering · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.1708.02722

Abstract

For Y ⊂ X a locally complete intersection of codimension p, Spencer Bloch [2] constructed the semi-regularity map π: H¹(N_Y/X) → H^p+1(Ω_X/k^p-1). As an analogue, we construct a map π: H¹(N_Y/X) → H^p+1(Ω_X/ℚ^p-1), without assuming local complete intersections. While the semi-regularity map π is expected to be injective, we show π is a zero map. We use this zero map to interpret how to eliminate obstructions to deforming cycles, an idea by Mark Green and Phillip Griffiths in [9].

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