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Title: Abelian orbifolds in dimension four and crepant resolutions via G-Hilbert schemes
Author: Muhvić, Sara
ISNI:       0000 0004 7425 6658
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2018
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We study the quotient X=C^4/G, where the group G ≅(Z/r)⊕3 ⊂ SL (4;C) acts by 1/r (1, -1, 0, 0) ⊕ 1/r (1, 0, -1, 0) ⊕ (1, 0, 0, -1). The affine quotient X=C^4/G is a Gorenstein hypersurface singularity (x_1 x_2 x_3 x_4=y^r). In this thesis, we give an explicit description of the G-Hilbert scheme G-HilbC^4 through its toric fan. We show that it is an irreducible toric variety that is a discrepant resolution of singularities of X. Furthermore, we construct a certain class of crepant resolutions of X, called the special crepant resolutions, that are obtained from the G-HilbC^4by a series of contractions of curves.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics