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      The tangent space of the punctual Hilbert scheme

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          Abstract

          The purpose of this paper is to study the Zariski tangent space of the punctual Hilbert scheme parametrizing subschemes of a smooth surface which are supported at a single point. We give a lower bound on the dimension of the tangent space in general and show the bound is sharp for subschemes of the affine plane cut out by monomials. Furthermore for monomial subschemes we give an explicit combinatorial formula for the dimension of the tangent space.

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          Journal
          2016-04-17
          Article
          1604.04915

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          14C05, 14J60
          math.AG

          Geometry & Topology

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