This book can form the basis of a second course in algebraic
geometry. As motivation, it takes concrete questions from
enumerative geometry and intersection theory, and provides
intuition and technique, so that the student develops the ability
to solve geometric problems. The authors explain key ideas,
including rational equivalence, Chow rings, Schubert calculus and
Chern classes, and readers will appreciate the abundant examples,
many provided as exercises with solutions available online.
Intersection is concerned with the enumeration of solutions of
systems of polynomial equations in several variables. It has been
an active area of mathematics since the work of Leibniz. Chasles'
nineteenth-century calculation that there are 3264 smooth conic
plane curves tangent to five given general conics was an important
landmark, and was the inspiration behind the title of this book.
Such computations were motivation for Poincare's development of
topology, and for many subsequent theories, so that intersection
theory is now a central topic of modern mathematics.
General
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