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Full-Text Articles in Mathematics
A Journey To Fuzzy Rings, Brett T. Ernst
A Journey To Fuzzy Rings, Brett T. Ernst
Electronic Theses and Dissertations
Enumerative geometry is a very old branch of algebraic geometry. In this thesis, we will describe several classical problems in enumerative geometry and their solutions in order to motivate the introduction of tropical geometry. Finally, fuzzy rings, a powerful algebraic framework for tropical and algebraic geometry is introduced.
Generalized Borcea-Voisin Construction, Jimmy Dillies
Generalized Borcea-Voisin Construction, Jimmy Dillies
Department of Mathematical Sciences Faculty Publications
C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the …
On Some Order 6 Non-Symplectic Automorphisms Of Elliptic K3 Surfaces, Jimmy J. Dillies
On Some Order 6 Non-Symplectic Automorphisms Of Elliptic K3 Surfaces, Jimmy J. Dillies
Department of Mathematical Sciences Faculty Publications
We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to a local analysis of the fixed loci. In particular, we determine the possible fixed loci and show that when the Picard lattice is fixed, K3 surfaces come in mirror pairs.