Constructing Stable Hilbert Bundles via Diophantine Approximation
Time: 2025-04-20
Published By: He Liu
Speaker(s): Biao Ma(BICMR)
Time: 14:30-15:30 April 21, 2025
Venue: Room 77201, Jingchunyuan 78, BICMR
On any complex smooth projective curve with positive genus, we construct Hilbert bundles that admit Hermitian–Einstein metrics. The main constructive step is by investigating the arithmetic property of the upper half plane in Bridgeland’s definition of stability conditions and its homological countparts. The main analytic ingredient in our proof is a notion called a geometrically well-approximable pair (X,θ). This notion compares a constant L(X) that can be bounded by the geometric information of the Riemann surface X with a constant L0(θ) that depends only on the arithmetic information of the irrational number θ. This notion helps us to apply the Diophantine approximation to Donaldson’s functional. This talk is based on a joint work with Yucheng Liu (CQU).
