Birational superrigidity and slope stability of Fano manifolds
نویسندگان
چکیده
منابع مشابه
Birational Unboundedness of Fano Threefolds
In this paper, we prove that the family of Fano threefolds with Picard number one is birationally unbounded.
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Smooth toric Fano varieties are classified up to dimension 4. In dimension 2, there are five toric Del Pezzo surfaces: P, P1×P1, and Si, the blowup of P in i points, for i = 1, 2, 3. There are 18 toric Fano 3-folds [2, 20] and 124 toric Fano 4-folds [4, 17]. In higher dimensions, little is known about them and many properties that hold in low dimensions are not known to hold in general. Let X b...
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We investigate birational boundedness of Fano varieties and Fano fibrations. We establish an inductive step towards birational boundedness of Fano fibrations via conjectures related to boundedness of Fano varieties and Fano fibrations. As corollaries, we provide approaches towards birational boundedness and boundedness of anti-canonical volumes of varieties of -Fano type. Furthermore, we show b...
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We prove that the family of Q-Fano threefolds with Picard number one is birationally unbounded.
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The minimal model program has greatly enhanced our knowledge on birational geometry of varieties of dimension 3 and higher. About the same time, the last two decades have also witnessed increasing interests in HyperKähler manifolds, a particular class of Calabi-Yau manifolds. One interest in this area, which we hope to treat in the future, is to investigate the behavior of the SYZ mirror conjec...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2013
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-013-1172-7