Algebraic Geometry: A Problem Solving ApproachAmerican Mathematical Soc., 1 févr. 2013 - 335 pages Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of ex |
Table des matières
Conics | 1 |
Cubic Curves and Elliptic Curves | 61 |
Higher Degree Curves | 129 |
Affine Varieties | 197 |
Projective Varieties | 271 |
Sheaves and Cohomology | 301 |
| 329 | |
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Expressions et termes fréquents
affine affine varieties algebraic geometry algebraic set algebraic variety An(k Bézout’s Theorem birational change of coordinates Chapter coefficients complex numbers compute conics in P2 Consider corresponding cubic curve curve in P2 define defined Definition Dehomogenize denote differential form dimension divisor element ellipse equation equivalence relation f and g field Find finite function field given goal homogeneous ideal homogeneous polynomials hyperbola inflection point integer intersection multiplicity inverse irreducible isomorphic j-invariant Let f linear mathematics matrix maximal ideal morphism notation Op(V open set open subset parabola plane R2 Pn(k point of intersection pole polynomial map presheaf previous exercise prime ideal Proj(R projective change projective plane projective space projective variety Prove rational function rational map real affine change ring homomorphism root sheaf Show singular point smooth cubic curve Spec(R subvariety Suppose tangent line tangent space transformation vector space Zariski topology zero set