Rational curves in holomorphic symplectic varieties and Gromov-Witten invariants
We use Gromov-Witten theory to study rational curves in holomorphic symplectic varieties. We present a numerical criterion for the existence of uniruled divisors swept out by rational curves in the primitive curve class of a very general holomorphic symplectic variety of K3[n] type. We also classify...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1 December 2019
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| In: |
Advances in mathematics
Year: 2019, Volume: 357, Pages: 1-28 |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2019.106829 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.aim.2019.106829 Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S0001870819304463 
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| Author Notes: | Georg Oberdieck, Junliang Shen, Qizheng Yin |
| Summary: | We use Gromov-Witten theory to study rational curves in holomorphic symplectic varieties. We present a numerical criterion for the existence of uniruled divisors swept out by rational curves in the primitive curve class of a very general holomorphic symplectic variety of K3[n] type. We also classify all rational curves in the primitive curve class of the Fano variety of lines in a very general cubic 4-fold, and prove the irreducibility of the corresponding moduli space. Our proofs rely on Gromov-Witten calculations by the first author, and in the Fano case on a geometric construction of Voisin. In the Fano case a second proof via classical geometry is sketched. |
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| Item Description: | Gesehen am 14.01.2025 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2019.106829 |