Intersection Theory
Chow groups, Fulton–MacPherson, and Schubert calculus.
Intersection Theory. Chow groups, Fulton–MacPherson, and Schubert calculus.
Foundations and canonical references
The standard treatments of intersection theory approach the subject from complementary angles. Fulton, Intersection Theory (1998) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Eisenbud, 3264 and All That: A Second Course in Algebraic Geometry (2016) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for intersection theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1998Intersection Theoryfulton-1998
- textbook · primary · 20163264 and All That: A Second Course in Algebraic Geometryeisenbud-2016, harris-2016
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