Undergraduate Algebraic GeometryCambridge University Press, 15.12.1988 - 129 Seiten Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory. |
Inhalt
Playing with plane curves | 9 |
2 Cubics and the group law | 27 |
Curves and their genus | 43 |
The category of affine varieties | 48 |
4 Functions on varieties | 66 |
Applications | 79 |
6 Tangent space and nonsingularity dimension | 94 |
7 The 27 lines on a cubic surface | 102 |
8 Final comments | 114 |
| 129 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
A¹k affine piece affine varieties algebraic geometry algebraic set algebraic subsets algebraically closed algebraically independent bijection birational coefficients collinear commutative algebra complex consider contains contradiction coordinates Corollary corresponding cubic curve cubic surface cuspidal cubic deduce defined definition degree element equation equivalence example exists field extension field of fractions finite field genus given group law hence Hint hypersurface infinity inflexion point inverse isomorphism k-algebra homomorphism k-valued points Lemma linear forms map f matrix maximal ideal meets monic morphism multiple Noetherian nondegenerate conic nonempty nonzero Nullstellensatz open set open subset parametrised plane curve polynomial function polynomial map prime projective varieties proof Proposition prove quadratic form quadric rational functions rational map singular Spec subvariety suppose tangent space Theorem theory vanish variable write Zariski topology zero