Rick Miranda works on algebraic geometry and has written expositions of algebraic curves and elliptic surfaces. His Colorado State University page identifies both the research field and his books.[ref]
In The Basic Theory of Elliptic Surfaces by Rick Miranda, a pencil of plane cubics gives a concrete surface construction. Blowing up its nine base points resolves the rational map to the parameter line and produces an elliptic fibration. The example connects equations for curves, blowups and the geometry of an entire surface.[ref]
Figure 1.
Rick Miranda
. Portrait identified by the linked primary author or institutional profile. Source.

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