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Regularity of small powers

HDHailong Dao
•Posted on May 20, 2026
Difficulty
3 / 5
Problem Status
Open
Keywords
IDEALSCASTELNUOVO-MUMFORD REGULARITY
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Let KKK be a field and R=K[x,y]R=K[x,y]R=K[x,y]. Find:

lim inf⁡reg(I)+reg(I3)−2reg(I2)d\liminf \frac{reg(I)+reg(I^3)-2reg(I^2)}{d} liminfdreg(I)+reg(I3)−2reg(I2)​

where III runs over all homogenous RRR-ideals equi-generated in degree d>0d>0d>0.

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