Algebraic Geometry: A First CourseSpringer Science & Business Media, 11 de nov. 2013 - 330 pàgines This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988. It is intended to be, as the title suggests, a first introduction to the subject. Even so, a few words are in order about the purposes of the book. Algebraic geometry has developed tremendously over the last century. During the 19th century, the subject was practiced on a relatively concrete, down-to-earth level; the main objects of study were projective varieties, and the techniques for the most part were grounded in geometric constructions. This approach flourished during the middle of the century and reached its culmination in the work of the Italian school around the end of the 19th and the beginning of the 20th centuries. Ultimately, the subject was pushed beyond the limits of its foundations: by the end of its period the Italian school had progressed to the point where the language and techniques of the subject could no longer serve to express or carry out the ideas of its best practitioners. |
Continguts
3 | |
A Note on Dimension Smoothness and Degree | 16 |
LECTURE | 17 |
Regular Maps | 21 |
LECTURE 3 | 33 |
5 | 35 |
Constructible Sets | 39 |
Universal Families of Hypersurfaces | 45 |
Further Topics Involving Smoothness and Tangent Spaces | 211 |
Blowups Nash Blowups and the Resolution of Singularities | 219 |
Bézouts Theorem | 227 |
LECTURE 19 | 239 |
Degrees of Some Grassmannians | 245 |
LECTURE 20 | 251 |
Multiplicity | 258 |
Resolution of Singularities for Curves | 264 |
LECTURE 7 | 72 |
Unirationality | 87 |
More General Determinantal Varieties | 111 |
Quotients | 123 |
ATTRIBUTES OF VARIETIES | 130 |
Immediate Examples | 138 |
LECTURE 12 | 151 |
LECTURE 5 | 152 |
Group Actions | 161 |
Syzygies | 168 |
LECTURE 14 | 174 |
Projective Tangent Spaces | 181 |
LECTURE 16 | 200 |
The Resolution of the Generic Determinantal Variety | 206 |
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Frases i termes més freqüents
algebraic automorphism birational blow-up closure codimension common zero locus complete intersection cone containing deduce defined definition determinantal variety dim(X disjoint dual Example Exercise F₁ fact Fano variety fiber finite follows Gauss map given Grassmannian Hilbert polynomial homogeneous polynomials hyperplane section ideal incidence correspondence inverse image irreducible of dimension isomorphic k-planes Lecture linear forms linear space linear subspace M₁ matrix Note open subset parametrized polynomials of degree projection map projective space projective tangent space projective variety Proposition quadric hypersurface quadric surface quotient rank rational map rational normal curve rational normal scroll regular map secant line secant variety Segre variety Show singular smooth point smooth quadric span subvariety tangent line Theorem twisted cubic twisted cubic curve union vanishing vector space Veronese map Veronese surface W₁ Z₁ Zariski tangent space