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Birational Geometry of Log Pairs.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Birational Geometry of Log Pairs./
作者:	Meng, Fanjun.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2022,
面頁冊數:	118 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-12, Section: B.
Contained By:	Dissertations Abstracts International83-12B.
標題:	Mathematics. -
ISBN:	9798438778905

Birational Geometry of Log Pairs.
Meng, Fanjun.

Birational Geometry of Log Pairs. - Ann Arbor : ProQuest Dissertations & Theses, 2022 - 118 p.

Source: Dissertations Abstracts International, Volume: 83-12, Section: B.

Thesis (Ph.D.)--Northwestern University, 2022.

This item must not be sold to any third party vendors.

In this dissertation, we study the birational geometry of log pairs over the field of complex numbers, with an emphasis on the positivity properties of log pairs and their applications.First, we study the nonvanishing conjecture in the minimal model program. We prove the nonvanishing conjecture for uniruled log canonical pairs of dimension $n$, assuming the nonvanishing conjecture for smooth projective varieties in dimension $n-1$.Second, we prove that pushforwards of klt pairs under morphisms to abelian varieties satisfy some positivity properties, which include global generation after pullback by an isogeny, the existence of the Chen--Jiang decompositions and so on. These are applied to some effective results for linear systems on irregular varieties.Third, we prove some vanishing and torsion-freeness results for higher direct images of adjoint pairs satisfying relative abundance and nefness conditions. We apply these to generic vanishing and weak positivity.Finally, we study some conjectures on the behavior of Kodaira dimension proposed by Popa. We prove an additivity result for the log Kodaira dimension of algebraic fiber spaces over abelian varieties, a superadditivity result for algebraic fiber spaces over varieties of maximal Albanese dimension, as well as a subadditivity result for log pairs over abelian varieties.

ISBN: 9798438778905Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Birational geometry

Birational Geometry of Log Pairs.
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500 $a Source: Dissertations Abstracts International, Volume: 83-12, Section: B.
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506 $a This item must not be sold to any third party vendors.
520 $a In this dissertation, we study the birational geometry of log pairs over the field of complex numbers, with an emphasis on the positivity properties of log pairs and their applications.First, we study the nonvanishing conjecture in the minimal model program. We prove the nonvanishing conjecture for uniruled log canonical pairs of dimension $n$, assuming the nonvanishing conjecture for smooth projective varieties in dimension $n-1$.Second, we prove that pushforwards of klt pairs under morphisms to abelian varieties satisfy some positivity properties, which include global generation after pullback by an isogeny, the existence of the Chen--Jiang decompositions and so on. These are applied to some effective results for linear systems on irregular varieties.Third, we prove some vanishing and torsion-freeness results for higher direct images of adjoint pairs satisfying relative abundance and nefness conditions. We apply these to generic vanishing and weak positivity.Finally, we study some conjectures on the behavior of Kodaira dimension proposed by Popa. We prove an additivity result for the log Kodaira dimension of algebraic fiber spaces over abelian varieties, a superadditivity result for algebraic fiber spaces over varieties of maximal Albanese dimension, as well as a subadditivity result for log pairs over abelian varieties.
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650 4 $a Theoretical mathematics. $3 3173530
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653 $a Positivity properties
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