Universiteit Leiden

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Deformations of nodal surfaces

Promotores: P. Stevenhagen, L. van Geemen Co-promotor: R.M. van Luijk

Yan Zhao
01 december 2016
Thesis in Leiden Repository

In this thesis, we studied the Hodge theory and deformation theory of nodal surfaces. We showed that nodal surfaces in the projective 3-space satisfy the infinitesimal Torelli property. We considered families of examples of even nodal surfaces, that is, those endowed with a double cover branched on the nodes. We gave a new geometrical construction of even 56-nodal sextic surfaces, while we proved, using existing constructions, that the sub-Hodge structure of type (1,26,1) on the double cover S of any even 40-nodal sextic surface cannot be simple. We also demonstrated ways to compute sheaves of differential forms on singular varieties using Saito's theory of mixed Hodge modules.