Bunches Alexander M Kasprzyk
نویسنده
چکیده
What follows is a summary of a recent paper by Berchtold and Hausen [BH03] in which the language of bunches applied to toric varieties is presented and investigated. I would like to thank Jaros law Wísniewski for drawing this paper to my attention and helping me appreciate the methods described. In order to motivate the definitions, we first present an example in which the weighted projected space P(w1, . . . , wn) is constructed. 1 Motivating Example Take K = Z, n ∈ N, and E = Z with standard basis {e1, . . . , en}. Let γ = Cone {e1, . . . , en} be the first quadrant in EQ. Choose w1, . . . , wn ∈ N and define Q : ei 7→ wi. We have (see Definitions 4 and 5) that Θ = {Q≥0} ⊂ KQ and cov(Θ) = {ρ1, . . . , ρn}, where ρi = Cone ei. Consider the short exact sequence 0 −→ M := ker Q ι ↪→ E Q −→ K −→ 0. (1) Let x = ∑n i=1 aiei ∈ E, then
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