2026-09-21T04:55:41Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/49684 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Nevins, Thomas A. Katz, Sheldon Nevins, Thomas A. Bradlow, Steven B. Schenck, Henry K. Li, Chunyi 2014-05-30T17:04:43Z 2014-05-30T17:04:43Z 2016-09-22T20:59:22Z 2014-05 2014-05-30T17:04:43Z 2014-05 The Hilbert scheme of $n$ points in a smooth del Pezzo surface $S$ parameterizes zero-dimensional subschemes with length $n$ on $S$. We construct a flat family of deformations of Hilb$^n S$ which can be conceptually understood as the family of Hilbert schemes of points on a family of noncommutative deformations of $S$. Further we show that each deformed Hilb$^n S$ carries a generically symplectic holomorphic Poisson structure. Moreover, the generic deformation of Hilb$^nS$ has a $(k+2)$-dimensional moduli space, where the del Pezzo surface is the blow up of projective plane at $k$ sufficiently general points; and each of the fibers is of the form that we construct. Our work generalizes results of Nevins-Stafford constructing deformations of the Hilbert scheme of points on the plane, and of Hitchin studying those deformations from the viewpoint of Poisson geometry. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2014-04-23T14:15:57Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Li_Chunyi.pdf: 405581 bytes, checksum: 10f052f247d1043296ec90877bd0f648 (MD5) Made available in DSpace on 2014-05-30T17:04:43Z (GMT). No. of bitstreams: 2 Chunyi_Li.pdf: 405593 bytes, checksum: aa9392e4ae905312c5e3ea5c429d35cb (MD5) license.txt: 4056 bytes, checksum: 62f1b0fac12c0a836bedc221fe2ffdf6 (MD5) Restriction data tranferred 2014-07-01T11:38:37-05:00 Original Data Group with Access UIUC Users [automated] Release Date: 2016-05-30 12:09:03 UTC Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Seth Robbins (robbins.sd@gmail.com) on 2014-05-30T17:09:34Z Item is restricted until 2016-05-30T17:09:03Z U of I Only Restriction Lifted for Item 49735 on 2016-09-22T20:59:22Z. http://hdl.handle.net/2142/49684 en Copyright 2014 Chunyi Li Hilbert scheme deformation theory del Pezzo surface Deformations of the Hilbert scheme of points on a del Pezzo surface text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD