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As of 2024, Fulton had supervised the doctoral work of 24 students at Brown, Chicago, and Michigan. Fulton is known as the author or coauthor of a number of popular texts, including Algebraic Curves and Representation Theory.
In 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. [1] 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 ...
Algebraic Geometry. Graduate Texts in Mathematics. Vol. 52. ISBN 0-387-90244-9. Appendix A. William Fulton (1998). Intersection Theory (2nd ed.). Springer. ISBN 9780387985497. Algebraic Curves: An Introduction To Algebraic Geometry, by William Fulton with Richard Weiss. New York: Benjamin, 1969.
In mathematics, the Fulton–Hansen connectedness theorem is a result from intersection theory in algebraic geometry, for the case of subvarieties of projective space with codimension large enough to make the intersection have components of dimension at least 1. It is named after William Fulton and Johan Hansen, who proved it in 1979.
666841088 The number of quadric surfaces tangent to 9 given quadric surfaces in general position in 3-space (Schubert 1879, p.106) (Fulton 1984, p. 193) 5819539783680 The number of twisted cubic curves tangent to 12 given quadric surfaces in general position in 3-space (Schubert 1879, p.184) (S. Kleiman, S. A. Strømme & S. Xambó 1987)
In algebraic geometry, the Chow groups (named after Wei-Liang Chow by Claude Chevalley ) of an algebraic variety over any field are algebro-geometric analogs of the homology of a topological space. The elements of the Chow group are formed out of subvarieties (so-called algebraic cycles ) in a similar way to how simplicial or cellular homology ...
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In general this is an algebraic stack, and is a Deligne–Mumford stack for or =, or =, (in other words when the automorphism groups of the curves are finite). This moduli stack has a completion consisting of the moduli stack of stable curves (for given g {\displaystyle g} and n {\displaystyle n} ), which is proper over Spec Z .