Decomposing Birational Morphisms Between Smooth Threefolds: The Picard Number Two Case

A question proposed by Kollár asks whether a projective birational morphism between smooth projective $3$-folds can be decomposed into a sequence of smooth blow-downs and flops. We give an affirmative answer to this question when the relative Picard number is $2$.

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Publication Details

Journal
Taiwanese Journal of Mathematics
Published
2025-04-06
DOI
https://doi.org/10.11650/tjm/250401
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

Decomposing Birational Morphisms Between Smooth Threefolds: The Picard Number Two Case

Chen Jiang
3 links
Taiwanese Journal of Mathematics
Algebraic Geometry and Number Theory
article

Decomposing Birational Morphisms Between Smooth Threefolds: The Picard Number Two Case

Chen Jiang
article en

Abstract

A question proposed by Kollár asks whether a projective birational morphism between smooth projective $3$-folds can be decomposed into a sequence of smooth blow-downs and flops. We give an affirmative answer to this question when the relative Picard number is $2$.

Taiwanese Journal of MathematicsVol. 29(6)
Fudan University (CN)
Openalex Percentile: Top 88%
Algebraic Geometry and Number Theory
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Decomposing Birational Morphisms Between Smooth Threefolds: The Picard Number Two Case — Chen Jiang · Taiwanese Journal of Mathematics (2025) | TGRS Research Map | TGRS