Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.
0 有用 zz_flying 2013-01-25 12:44:58
简练,跟作者其它的书一样不好读;不过在toric variety入门书中还是最好的
0 有用 beren 2011-10-19 16:29:24
若想从SYZ入手来看Mirror Symmetry,这本可说是必读
0 有用 爱吃胡萝卜🥕 2023-03-21 23:39:17 美国
很好的一本小书,需要一点AG背景。主要是要对divisor和line bundle有一些理解。感觉其实不太需要Toric geometry的背景,但有的话会有很大帮助。(本科的时候真不知道Fulton这么有名,早知道怎么样得去听一节他的课。)
0 有用 爱吃胡萝卜🥕 2023-03-21 23:39:17 美国
很好的一本小书,需要一点AG背景。主要是要对divisor和line bundle有一些理解。感觉其实不太需要Toric geometry的背景,但有的话会有很大帮助。(本科的时候真不知道Fulton这么有名,早知道怎么样得去听一节他的课。)
0 有用 zz_flying 2013-01-25 12:44:58
简练,跟作者其它的书一样不好读;不过在toric variety入门书中还是最好的
0 有用 beren 2011-10-19 16:29:24
若想从SYZ入手来看Mirror Symmetry,这本可说是必读