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Titlebook: Classification of Higher Dimensional Algebraic Varieties; Christopher D. Hacon,Sándor Kovács Textbook 2010 Birkhäuser Basel 2010 Dimension

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Researching Intimacy in Familiesimensional varieties one must put conditions on the admissible families that restrict the kind of families and not only the kind of fibers that are allowed. This is perhaps better understood through an example of bad behavior.
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https://doi.org/10.1057/9781137271372e of these spaces. Moduli theory strives to understand how algebraic varieties deform and degenerate. When studying moduli spaces we are interested in the geometry of the moduli space that reflects the behavior of the families parameterized by the given moduli space. In other words, we are interested in the geometry of ..
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Oberwolfach Seminarshttp://image.papertrans.cn/c/image/227214.jpg
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Preliminariesadopt similar conventions for ℤ, ℚ, ℝ and ℂ and ≥ 0, ≤ 0, > 0 and < 0. We will write . ≫ 0 for any sufficiently big integerm . ∈ ℤ and 0 < ε ≪ 1 for any sufficiently small positive real number ε ∈ ℝ.. The . of . ∈ ℝ is ⌊.⌋ = max{. ∈ ℤ|. ≤ .}. The . of . ∈ ℝ is ⌈.⌉ = - ⌊-.⌋ and the . of . ∈ if {.} = . - ⌊.⌋.
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Introductionfective), then there exists a finite sequence . of well-understood birational maps known as flips and divisorial contractions such that . is a minimal model, i.e., . is nef (respectively . has the structure of a Mori fiber space, i.e., there is a morphism . such that . is relatively ample over .).
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Families and moduli functorsimensional varieties one must put conditions on the admissible families that restrict the kind of families and not only the kind of fibers that are allowed. This is perhaps better understood through an example of bad behavior.
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William Yat Wai Lo,Felix Sai Kit NgFor an excellent introduction to this topic the reader is urged to take a thorough look at Miles Reid’s . [Rei87]. Here we will only briefly touch on the subject.
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