University of Illinois Urbana-Champaign

Enumerative invariants for local Calabi-Yau threefolds

Choi, Jinwon

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Choi_Jinwon.pdf

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https://hdl.handle.net/2142/34220

Description

Title
Enumerative invariants for local Calabi-Yau threefolds
Author(s)
Choi, Jinwon
Issue Date
2012-09-18T21:06:28Z
Director of Research (if dissertation) or Advisor (if thesis)
Katz, Sheldon
Doctoral Committee Chair(s)
Haboush, William J.
Committee Member(s)
  • Katz, Sheldon
  • Schenck, Henry K.
  • Nevins, Thomas A.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2012-09-18T21:06:28Z
Keyword(s)
  • Bogomol'nyi-Prasad-Sommerfeld (BPS) invariant
  • moduli space
  • equivariant sheaf
  • toric variety
  • wall crossing
Abstract
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.
Graduation Semester
2012-08
Permalink
http://hdl.handle.net/2142/34220
Copyright and License Information
Copyright 2012 Jinwon Choi

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