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1921•American Mathematical MonthlyRequires access

Plane Algebraic Curves.

Harold Hilton

Open publisher page 33 citations

Abstract

I. History of algebraic curves.- 1. Origin and generation of curves.- 2. Synthetic and analytic geometry.- 3. The development of projective geometry.- II. Investigation of curves by elementary algebraic methods.- 4. Polynomials.- 5. Definition and elementary properties of plane algebraic curves.- 6. The intersection of plane curves.- 7. Some simple types of curves.- III. Investigation of curves by resolution of singularities.- 8. Local investigations.- 9. Global investigations.- Bibliography.- Index.

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What this paper is about

I. History of algebraic curves.- 1. Origin and generation of curves.- 2. Synthetic and analytic geometry.- 3. The development of projective geometry.- II. Investigation of curves by elementary algebraic methods.- 4. Polynomials.- 5. Definition and elementary properties of plane algebraic curves.- 6. The intersection of plane curves.- 7. Some simple types of curves.- III. Investigation of curves by resolution of singularities.- 8. Local investigations.- 9. Global investigations.- Bibliography.- Index.

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OpenAlex reports 33 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

I. History of algebraic curves.- 1. Origin and generation of curves.- 2. Synthetic and analytic geometry.- 3. The development of projective geometry.- II. Investigation of curves by elementary algebraic methods.- 4. Polynomials.- 5. Definition and elementary properties of plane algebraic curves.- 6. The intersection of plane curves.- 7. Some simple types of curves.- III. Investigation of curves by resolution of singularities.- 8. Local investigations.- 9. Global investigations.- Bibliography.- Index.

Key concepts: Plane curve, Algebraic curve, Mathematics, Algebraic surface, Family of curves, Intersection (aeronautics), Plane (geometry), Gravitational singularity

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