Enriques–Kodaira classificationIn mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes. For each of these classes, the surfaces in the class can be parametrized by a moduli space. For most of the classes the moduli spaces are well understood, but for the class of surfaces of general type the moduli spaces seem too complicated to describe explicitly, though some components are known. Max Noether began the systematic study of algebraic surfaces, and Guido Castelnuovo proved important parts of the classification.
Intersection theoryIn mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. The theory for varieties is older, with roots in Bézout's theorem on curves and elimination theory. On the other hand, the topological theory more quickly reached a definitive form. There is yet an ongoing development of intersection theory. Currently the main focus is on: virtual fundamental cycles, quantum intersection rings, Gromov-Witten theory and the extension of intersection theory from schemes to stacks.
Henry Frederick BakerHenry Frederick Baker ( – ), est un mathématicien britannique, qui travailla principalement en géométrie algébrique, mais aussi connu pour ses contributions aux équations aux dérivées partielles, liées à ce qui allait devenir connu sous le nom de solitons, et aux groupes de Lie. Il est né à Cambridge, de Henty Baker, un majordome, et Sarah Ann Britham. Il a fait ses études à la avant de remporter une bourse d'études au St John's College de Cambridge, en . Baker est diplômé en tant que Senior Wrangler à l'issue du Tripos en 1887 entre crochets avec 3 autres.
Hodge index theoremIn mathematics, the Hodge index theorem for an algebraic surface V determines the signature of the intersection pairing on the algebraic curves C on V. It says, roughly speaking, that the space spanned by such curves (up to linear equivalence) has a one-dimensional subspace on which it is positive definite (not uniquely determined), and decomposes as a direct sum of some such one-dimensional subspace, and a complementary subspace on which it is negative definite.
Géométrie birationnellethumb|right|Le cercle est birationnellement équivalent à la droite. Un exemple d'application birationnelle est la projection stéréographique, représentée ici ; avec les notations du texte, P a pour abscisse 1/t. En mathématiques, la géométrie birationnelle est un domaine de la géométrie algébrique dont l'objectif est de déterminer si deux variétés algébriques sont isomorphes, à un ensemble négligeable près. Cela revient à étudier des applications définies par des fonctions rationnelles plutôt que par des polynômes, ces applications n'étant pas définies aux pôles des fonctions.
Dimension of an algebraic varietyIn mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways. Some of these definitions are of geometric nature, while some other are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply also to any algebraic set. Some are intrinsic, as independent of any embedding of the variety into an affine or projective space, while other are related to such an embedding.
