Deformations of nodal surfaces

Leiden Repository

Deformations of nodal surfaces

Type: Doctoral Thesis
Title: Deformations of nodal surfaces
Author: Zhao, Y.
Issue Date: 2016-12-01
Keywords: Infinitesimal Torelli theorem
Even nodal surfaces
Mixed Hodge modules
Abstract: 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.
Promotor: Supervisor: P. Stevenhagen, L. van Geemen Co-Supervisor: R.M. van Luijk
Faculty: Science
University: Leiden
Handle: http://hdl.handle.net/1887/44549
 

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