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Full-Text Articles in Mathematics
On The Geometry Of The Moduli Space Of Certain Lattice Polarized K3 Surfaces And Their Picard-Fuchs Operators, Michael T. Schultz
On The Geometry Of The Moduli Space Of Certain Lattice Polarized K3 Surfaces And Their Picard-Fuchs Operators, Michael T. Schultz
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
K3 surfaces have a long and rich study in mathematics, and more recently in physics via string theory. Often, K3 surfaces come in multiparameter families - the parameters describing these surfaces fit together to form their own geometric space, a so-called moduli space. In particular, the moduli spaces of K3 surfaces equipped with a lattice polarization can sometimes be constructed explicitly, which subsequently reveals important information about the original K3 surface.
In this work, we construct such families explicitly from certain rational elliptic surfaces via the so-called mixed-twist construction of Doran & Malmendier, which in turn produces the moduli …
Classification Of Jacobian Elliptic Fibrations On A Special Family Of K3 Surfaces Of Picard Rank Sixteen, Thomas Hill
Classification Of Jacobian Elliptic Fibrations On A Special Family Of K3 Surfaces Of Picard Rank Sixteen, Thomas Hill
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
K3 surfaces are an important tool used to understand the symmetries in physics that link different string theories, called string dualities. For example, heterotic string theory compactified on an elliptic curve describes a theory physically equivalent to (dual to) F-theory compactified on a K3 surface. In fact, M-theory, the type IIA string, the type IIB string, the Spin(32)/Z2 heterotic string, and the E8 x E8 heterotic string are all related by compactification on Calabi-Yau manifolds.
We study a special family of K3 surfaces, namely a family of rank sixteen K3 surfaces polarized by the lattice H⊕E …