Openness of klt type in flat families
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Is being of klt type open in a flat complex family? The counterexample target has a klt-type special fiber but nearby fibers that are not of klt type, arising from a determinantal family after T=sE.
Why it matters and what counts as progress
Why it matters: It tests whether a birational singularity property persists under deformation without additional hypotheses.
What counts as progress: An explicit flat family where klt type fails to persist, or an openness theorem with the additional assumptions that prevent that failure.
How the problem developed
- 21 May 2026 · Counterexample [1]
Jihao Liu; ChatGPT Pro 5.5 and Rethlas Answered Han and Jiang’s question by constructing a flat family whose special fiber is of klt type while its nonzero fibers are not.
AI contribution
A question on klt type varieties of Han and Jiang
A flat complex family made by substituting T=sE into Singh’s determinantal family has a klt-type special fiber and nearby fibers that are not of klt type. It gives a negative answer to Han and Jiang’s Problem 4.6.
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