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...geometry (such as [[Gröbner basis]]), [[Torelli set]]s and [[toric variety|toric varieties]], and [[history of mathematics]]. He is also known for several t * With John Little, Henry Schenck: ''Toric Varieties'', American Mathematical Society 2011 ...

...v=alg-geom/9202004|s2cid=9228037}}</ref> Notice the vector space of global sections has dimension<math display="block">\dim { \Gamma (\mathbb {P} ^{4},{\mathca ...ies]] - first general construction of mirror varieties for Calabi-Yau's in toric varieties ...

...hor-link=Simon Donaldson|year=2002|title=Scalar curvature and stability of toric varieties |url=http://projecteuclid.org/euclid.jdg/1090950195|journal=[[Jou ...of K-stability in terms of convex functions on the moment polytope of the toric variety, as was observed by Donaldson in his first paper on K-stability.<re ...

...differentiable manifolds.<ref>{{Cite arXiv|title = Global quotients among toric Deligne-Mumford stacks|eprint=1302.0385 |date = 2013-02-02|first1 = Megumi| ...U)</math> is a reduced ring, i.e., <math>X</math> has no nonzero nilpotent sections.}} ...

...not locally free, and to do this Kobayashi proved a vanishing theorem for sections of Hermite–Einstein vector bundles. ...ournal |doi=10.4310/jdg/1090950195|title=Scalar Curvature and Stability of Toric Varieties |year=2002 |last1=Donaldson |first1=S.K. |journal=Journal of Diff ...