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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 algebraic geometry, Brill–Noether theory, introduced by Alexander von Brill and Max Noether , is the study of special divisors, certain divisors on a curve C that determine more compatible functions than would be predicted. In classical language, special divisors move on the curve in a "larger than expected" linear system of divisors.
The characteristic linear system of a family of curves on an algebraic surface Y for a curve C in the family is a linear system formed by the curves in the family that are infinitely near C. [ 4 ] In modern terms, it is a subsystem of the linear system associated to the normal bundle to C ↪ Y {\displaystyle C\hookrightarrow Y} .
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 ...
The study of moduli spaces of curves, maps and other geometric objects, sometimes via the theory of quantum cohomology. The study of quantum cohomology, Gromov–Witten invariants and mirror symmetry gave a significant progress in Clemens conjecture. Enumerative geometry is very closely tied to intersection theory. [1]
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.
A divisor on a Riemann surface C is a formal sum = of points P on C with integer coefficients. One considers a divisor as a set of constraints on meromorphic functions in the function field of C, defining () as the vector space of functions having poles only at points of D with positive coefficient, at most as bad as the coefficient indicates, and having zeros at points of D with negative ...
Fermat curve; Bézout's theorem; Brill–Noether theory; Genus (mathematics) Riemann surface; Riemann–Hurwitz formula; Riemann–Roch theorem; Abelian integral; Differential of the first kind; Jacobian variety. Generalized Jacobian; Moduli of algebraic curves; Hurwitz's theorem on automorphisms of a curve; Clifford's theorem on special divisors
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