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Symplectic geometry and rationally connected 4-folds
Published/Copyright:
April 4, 2013
Abstract
We study some symplectic geometric aspects of rationally connected 4-folds. As a corollary, we prove that any smooth projective 4-fold symplectic deformation equivalent to a Fano 4-fold of pseudo-index at least 2 or a rationally connected 4-fold whose second Betti number is 2 is rationally connected.
I would like to thank Tom Graber, Yongbin Ruan, Jason Starr, Claire Voisin, and Aleksey Zinger for discussions about various parts of the project, Zhiyuan Li and Letao Zhang for their encouragement, and Chenyang Xu for providing the key argument in Lemma 5.4 using “fake projective spaces”.
Received: 2012-10-14
Published Online: 2013-4-4
Published in Print: 2015-1-1
© 2015 by De Gruyter
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- Frontmatter
- Toric varieties, monoid schemes and cdh descent
- The kernel of the reciprocity map of varieties over local fields
- Tropical geometry over higher dimensional local fields
- Coleman–Gross height pairings and the p-adic sigma function
- On main conjectures in non-commutative Iwasawa theory and related conjectures
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Articles in the same Issue
- Frontmatter
- Toric varieties, monoid schemes and cdh descent
- The kernel of the reciprocity map of varieties over local fields
- Tropical geometry over higher dimensional local fields
- Coleman–Gross height pairings and the p-adic sigma function
- On main conjectures in non-commutative Iwasawa theory and related conjectures
- Ahlfors–Weill extensions in several complex variables
- Double solid twistor spaces II: General case
- Symplectic geometry and rationally connected 4-folds
