Prof. Miranda's main field of interest is Algebraic Geometry,
which is, broadly speaking, the study of curves, surfaces, etc.
which are defined by the vanishing of one or several polynomials.
He has written articles and/or directed research in the following areas.
- Elliptic Surfaces
- Geometric Invariant Theory
- Classification and Degenerations of Surfaces
- Finite Coverings of Algebraic Varieties
- Integral Quadratic Forms
- Resolutions of Singularities
- Toric Geometry
- Gaussian Maps for Curves
- Graph Curves
- Fano Threefolds
- Quantum Cohomology
- Linear Systems of Plane Curves