2026-09-20T22:18:43Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/34220 2023-07-10 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Katz, Sheldon Haboush, William J. Katz, Sheldon Schenck, Henry K. Nevins, Thomas A. Choi, Jinwon 2012-09-18T21:06:28Z 2012-09-18T21:06:28Z 2012-08 2012-09-18T21:06:28Z 2012-08 This thesis consists of three parts. In the first part, we compute the topological Euler characteristics of the moduli spaces of stable sheaves of dimension one on the total space of rank 2 bundle on P1 whose determinant is O(−2). We count the torus fixed stable sheaves of low degrees and show the results verify the predictions in physics and the local Gromov-Witten theory. In the second part, we compute the Poincar´e polynomial of the moduli space of stable sheaves with Hilbert polynomial 4n + 1 on P2. This is done by classifying all torus fixed points in the moduli space and computing the torus representation of their tangent spaces. The result is also in agreement with a computation in physics. In the third part, we propose an algorithm to compute the Euler characteristics of the moduli spaces of stable sheaves of dimension one on P2 by means of Joyce’s wall crossing formula. The wall crossing takes place over the moduli spaces of α-stable pairs as the stability parameter α varies. The results verify a conjecture in the theory of curve counting invariants motivated by physics. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-07-03T13:56:39Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 Choi_Jinwon.tex: 237201 bytes, checksum: 0a9526a53640d29bb33bbf61afe3efa0 (MD5) Choi_Jinwon.pdf: 705606 bytes, checksum: 277d3cd8d4541bae15511ebfa7a0c583 (MD5) Made available in DSpace on 2012-09-18T21:06:28Z (GMT). No. of bitstreams: 3 Choi_Jinwon.pdf: 705021 bytes, checksum: 01562fa202d9b66961ad83b0c8991e60 (MD5) license.txt: 4059 bytes, checksum: dbd81eac71b5dcaf71c9da236d4fcec5 (MD5) Choi_Jinwon.tex: 237368 bytes, checksum: 2954d1b0c83fd288ee821224745cc146 (MD5) http://hdl.handle.net/2142/34220 en Copyright 2012 Jinwon Choi Bogomol'nyi-Prasad-Sommerfeld (BPS) invariant moduli space equivariant sheaf toric variety wall crossing Enumerative invariants for local Calabi-Yau threefolds Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD