Enumerative invariants for local Calabi-Yau threefolds

["Bogomolnyi-Prasad-Sommerfeld (BPS) invariant";moduli space;equivariant sheaf;toric\rvariety;wall crossing

Choi, Jinwon

关键词: ["Bogomolnyi-Prasad-Sommerfeld (BPS) invariant";    moduli space;    equivariant sheaf;    toric\rvariety;    wall crossing;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/34220/Choi_Jinwon.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This thesis consists of three parts. In the first part, we compute the topological Eulercharacteristics of the moduli spaces of stable sheaves of dimension one on the total space ofrank 2 bundle on P1 whose determinant is O(−2). We count the torus fixed stable sheavesof 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 ofthe moduli space of stable sheaves with Hilbert polynomial 4n + 1 on P2. This is done byclassifying all torus fixed points in the moduli space and computing the torus representationof their tangent spaces. The result is also in agreement with a computation in physics. In thethird 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.