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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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发表于 2025-3-21 18:47:17 | 显示全部楼层 |阅读模式
书目名称Classification of Higher Dimensional Algebraic Varieties
编辑Christopher D. Hacon,Sándor Kovács
视频video
概述Introductory text to an advanced topic of active research.Includes supplementary material:
丛书名称Oberwolfach Seminars
图书封面Titlebook: Classification of Higher Dimensional Algebraic Varieties;  Christopher D. Hacon,Sándor Kovács Textbook 2010 Birkhäuser Basel 2010 Dimension
描述This book focuses on recent advances in the classification of complex projective varieties. It is divided into two parts. The first part gives a detailed account of recent results in the minimal model program. In particular, it contains a complete proof of the theorems on the existence of flips, on the existence of minimal models for varieties of log general type and of the finite generation of the canonical ring. The second part is an introduction to the theory of moduli spaces. It includes topics such as representing and moduli functors, Hilbert schemes, the boundedness, local closedness and separatedness of moduli spaces and the boundedness for varieties of general type.The book is aimed at advanced graduate students and researchers in algebraic geometry.
出版日期Textbook 2010
关键词Dimension; Divisor; Grad; algebraic geometry; algebraic varieties; minimal model; moduli space; projective
版次1
doihttps://doi.org/10.1007/978-3-0346-0290-7
isbn_softcover978-3-0346-0289-1
isbn_ebook978-3-0346-0290-7Series ISSN 1661-237X Series E-ISSN 2296-5041
issn_series 1661-237X
copyrightBirkhäuser Basel 2010
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发表于 2025-3-21 21:39:22 | 显示全部楼层
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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Log terminal models(X; Δ + C = S + A +B +C) be a ℚ-factorial dlt pair with S = ⌊Δ⌋, such that K. + Δ +C is nef over U and .+A/U) contains no non-klt centers of (X,Δ + C). Let Φ.: X. → X. be a sequence of flips and divisorial contractions over U for the (K. + Δ)-mmp over U with scaling of C.
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Subvarieties of moduli spacese 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 intereste
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Researching Higher Education in Asiaadopt 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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Researching Intercultural Learning(X; Δ + C = S + A +B +C) be a ℚ-factorial dlt pair with S = ⌊Δ⌋, such that K. + Δ +C is nef over U and .+A/U) contains no non-klt centers of (X,Δ + C). Let Φ.: X. → X. be a sequence of flips and divisorial contractions over U for the (K. + Δ)-mmp over U with scaling of C.
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