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Nicholas Shepherd-Barron works in various aspects of algebraic geometry, such as: singularities in the Minimal Model Program; compactification of moduli spaces, and the rationality of orbit spaces - including the moduli spaces of curves of genus 4 and 6. Other aspects of Nicholas’ interests within this field include the geography of algebraic surfaces in positive characteristic, including a proof of Raynaud's conjecture; canonical models (in the sense of birational geometry, not that of Shimura varieties) of moduli spaces of abelian varieties; the Schottky problem at the boundary; the relation between algebraic groups and del Pezzo surfaces; and the period map for elliptic surfaces. He was elected Fellow of the Royal Society in 2006.

Research interests

  • Algebraic geometry