Analytic Bertini restriction for multiplier ideals
Follow the latest progress by email.
For a plurisubharmonic weight on a product of polydiscs, does the ambient multiplier ideal restrict to the fibre multiplier ideal outside a pluripolar parameter set? This asks for a smaller exceptional set than a merely Lebesgue-null set.
Why it matters and what counts as progress
Why it matters: Replacing a null exceptional set by a pluripolar one gives a stronger analytic description of where multiplier-ideal restriction can fail.
What counts as progress: Prove the pluripolar exceptional-set bound in the local setting or extend the restriction theorem to holomorphic fibrations.
How the problem developed
Takeo Ohsawa and Kenshō Takegoshi Established an L² extension theorem that yields one inclusion in the restriction formula for multiplier ideals on fibres.
Mingchen Xia Proved an analytic Bertini restriction result for projective fibrations, leaving the local case open.
- 28 Jul 2026 · Reported claim [3]
Mingchen Xia, with GPT-5.6 Sol proof work Proved equality of ambient and fibre multiplier ideals outside a pluripolar parameter set in the local setting and for holomorphic fibrations.
AI contribution
Analytic Bertini theorem II --- The local case
For a plurisubharmonic weight on a product of polydiscs, Xia proves that the ambient multiplier ideal restricts to the fiber multiplier ideal outside a pluripolar parameter set. The paper also extends the result to holomorphic fibrations.
Sources
Website timeline
Publication dates and editorial changes.
AI-developed proof details support local analytic Bertini theorem