Moduli Spaces for Rational Elliptic Surfaces - of Index 1 and 2

Explore the fascinating world of rational elliptic surfaces in this 51-minute lecture by Rick Miranda from Colorado State University. Delve into the theoretical and practical importance of elliptic surfaces in the classification and study of surfaces. Learn about Jacobian surfaces, constructed by blowing up base points in a general pencil of plane cubics, and their moduli spaces. Discover how rational elliptic surfaces without sections can be obtained using pencils of curves with specific degrees and base point multiplicities. Examine the concept of multiple fibers and fibration index in rational elliptic surfaces. Investigate recent developments in computing GIT stability for pencils with index 2 and the construction of moduli spaces using toric methods, as presented in joint work with A. Zanardini.