Published 2015
| Published + Submitted
Journal Article
Open
Picard Groups on Moduli of K3 Surfaces with Mukai Models
- Creators
- Greer, Francois
- Li, Zhiyuan
- Tian, Zhiyu
Abstract
We discuss the Picard group of the moduli space K_g of quasi-polarized K3 surfaces of genus g≤12 and g≠11. In this range, K_g is unirational, and a general element in K_g is a complete intersection with respect to a vector bundle on a homogenous space, by the work of Mukai. In this paper, we find generators for the Picard group Pic_Q(K_g) using the Noether–Lefschetz (NL) theory. This verifies the NL conjecture on the moduli of K3 surfaces in these cases.
Additional Information
© 2014 The Author(s). Published by Oxford University Press. Received March 3, 2014. Revision received August 5, 2014. Accepted August 21, 2014. First published online: September 26, 2014. We have benefited from conversations with Brendan Hassett and Jun Li. We are very grateful to Arie Peterson for his useful comments and providing us the relation of NL divisors in Remark 4.2. We would also like to thank the referees for all their comments and suggestions.Attached Files
Published - Int_Math_Res_Notices-2015-Greer-7238-57.pdf
Submitted - 1402.2330v3.pdf
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1402.2330v3.pdf
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Additional details
- Eprint ID
- 62090
- Resolver ID
- CaltechAUTHORS:20151113-080819027
- Created
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2015-11-18Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field