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Fellowship of the Ring
A worldwide commutative algebra seminar
Next talk, April 8th, 2026
Next talk, April 8th, 2026
3:30pm Eastern = 12:30pm Pacific
NOTE EARLIER SPECIAL TIME
Antoni Rangachev (IMJ-PRG & IMI-BAS)
Antoni Rangachev (IMJ-PRG & IMI-BAS)
Title: Rational powers of ideals and Hölder continuity
Title: Rational powers of ideals and Hölder continuity
Abstract: For a reduced complex analytic variety, one can define the sheaf of α-Hölder continuous meromorphic functions. This sheaf is a coherent subsheaf of the normalization sheaf. Using rational powers of the ideal of a certain diagonal, I will show that there are only finitely many rational numbers α∈(0,1] that determine all the relevant Hölder exponents. I will prove that an analytically irreducible curve is bi-α-Hölder homeomorphic to its normalization, where α is determined by the last characteristic exponent of a generic plane projection of the curve.I will also introduce the notion of α-Hölder equisingularity for flat families of complex analytic varieties. For families of curves, I will show that for sufficiently large α, α-Hölder equisingularity is equivalent to the existence of a strong simultaneous resolution. This is joint work in progress with François Bernard (University of Toronto).
Abstract: For a reduced complex analytic variety, one can define the sheaf of α-Hölder continuous meromorphic functions. This sheaf is a coherent subsheaf of the normalization sheaf. Using rational powers of the ideal of a certain diagonal, I will show that there are only finitely many rational numbers α∈(0,1] that determine all the relevant Hölder exponents. I will prove that an analytically irreducible curve is bi-α-Hölder homeomorphic to its normalization, where α is determined by the last characteristic exponent of a generic plane projection of the curve.I will also introduce the notion of α-Hölder equisingularity for flat families of complex analytic varieties. For families of curves, I will show that for sufficiently large α, α-Hölder equisingularity is equivalent to the existence of a strong simultaneous resolution. This is joint work in progress with François Bernard (University of Toronto).
Scientific committee
Scientific committee
Michael K. Brown (Auburn)
Dale Cutkosky (Missouri)
David Eisenbud (Berkeley)
Irena Peeva (Cornell)
Claudia Polini (Notre Dame)
Claudiu Raicu (Notre Dame)
Karl Schwede (Utah)
Gregory G. Smith (Queen's University)
Bernd Ulrich (Purdue)
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