Tyurin degenerations of K3 surfaces

<p dir="ltr">This thesis focuses on Type II degenerations of K3 surfaces of degrees 2 and 4.</p><p dir="ltr">In Chapter 1 we lay out the necessary background material required in this work, beginning with the fundamentals of K3 surface theory and their moduli spaces. We also discuss the work of Friedman and Scattone and the relation this has to the current work. At the end of Chapter 1 we briefly discuss recent work of Alexeev and Engel to help describe families of degenerations of K3 surfaces.</p><p dir="ltr">In Chapter 2 we use results of Thompson to describe 4 explicit Type II degenerations of K3 surfaces of degree 2. From these constructions we build 18-dimensional families of the central fibers of Type II degenerations of degree 2 with two components. We also describe all stable models of these central fibers.</p><p dir="ltr">Chapter 3 explicitly builds 9 Type II degenerations of K3 surfaces of degree 4 using results of Shah. We then perform similar calculations to those performed in Chapter 2 to build 18-dimensional families of the central fibers of Type II degenerations of degree 4 with two components. We also describe all stable models of these central fibers.</p><p dir="ltr">To conclude the thesis, we briefly highlight in Chapter 4 several observations which we have made during this work. We also discuss some applications of the results of Chapters 2 and 3 to ongoing work in Mirror Symmetry.</p>