题目：Marked Hilbert–Chow Direct Images and the Wilson Loop

报告人：赵璐天，东京大学IPMU

时间：9月16日（周三）下午4点

地点：新楼310

摘要：Huang, Katz, Klemm, and Wang proposed a factorization of refined BPS invariants of compact elliptic Calabi–Yau threefolds in terms of Wilson-loop expectation values of the associated local theories. I will discuss a sheaf-theoretic approach to this proposal for a smooth Weierstrass Calabi–Yau threefold over (\mathbb P^2). Relative Fourier–Mukai transforms identify stable one-dimensional sheaves over smooth projected curves with rank-one torsion-free sheaves on elliptic surfaces, while the Göttsche–Soergel decomposition controls collisions of vertical point defects. Marked Hilbert–Chow direct images then provide geometric counterparts of the Wilson-loop coefficients, and Shioda's height formula explains the labels (k-3l) occurring in the Huang–Katz–Klemm–Wang expansion. I will also describe the compact calculation in class (H+f), the graph-section contribution in class (H+3f), and the remaining support problem over nonreduced projected curves.