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Rings of differential operators on (k,s)-th Tjurina algebras of singularities

  • Siyong Tao and Huaiqing Zuo EMAIL logo
Published/Copyright: November 14, 2024
Forum Mathematicum
From the journal Forum Mathematicum Volume 37 Issue 5

Abstract

In this paper, we give a description of differential operators on tensor products A ⊗ 𝕂 B , where A and B are finitely generated 𝕂 -algebras. We prove that any differential operator on A ⊗ 𝕂 B can be written as a finite sum of D 1 ⊗ D 2 , where D 1 and D 2 are differential operators on A and B, respectively. Moreover, we introduce a series of new invariants, the ( k , s ) -th Tjurina algebra A ( k , s ) ⁢ ( V ) for an isolated hypersurface singularity ( V , 𝟎 ) = ( V ⁢ ( f ) , 𝟎 ) ⊆ ( ℂ r , 𝟎 ) . We formulate a sharp upper estimate for the dimension of the ℂ -vector space of differential operators on A ( k , s ) ⁢ ( V ) of order at most 1, and we give lower and upper bounds for the dimension of the ℂ -vector space of differential operators on A ( k , s ) ⁢ ( V ) of order at most n.

Keywords: Differential operators; tensor product; isolated hypersurface singularity; invariants
MSC 2020: 14B05; 32S05

Communicated by Siegfried Echterhoff

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 12271280

Funding statement: Huaiqing Zuo is supported by the National Natural Science Foundation of China, Grant No. 12271280.

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Received: 2024-04-04
Revised: 2024-07-24
Published Online: 2024-11-14
Published in Print: 2025-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Rings of differential operators on (k,s)-th Tjurina algebras of singularities
  3. Cokernels of random matrix products and flag Cohen–Lenstra heuristic
  4. Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
  5. The L p -L q compactness of commutators of oscillatory singular integrals
  6. Determination of a pair of newforms from the product of their twisted central values
  7. Metrical properties of exponentially growing partial quotients
  8. Nonlinear operations and factorizations on a class of affine modulation spaces
  9. On algebraic degrees of certain exponential sums over finite fields
  10. The ranks of (a,b)-Fibonacci sequences and congruences for certain partition functions and Ramanujan's mock theta functions
  11. Dynamics of radial threshold solutions for generalized energy-critical Hartree equation
  12. Modular representations of GL2(𝔽𝑞) using calculus
  13. Bounding the number of p'-degree characters from below
  14. Existence and multiplicity of non-radial sign-changing solutions for a semilinear elliptic equation in hyperbolic space
  15. Duality theorems for polyanalytic functions
  16. Lower bounds for the number of number fields with Galois group GL2(𝔽ℓ)
  17. Cylindrical ample divisors on Du Val del Pezzo surfaces
https://doi.org/10.1515/forum-2024-0161
Keywords for this article
Differential operators; tensor product; isolated hypersurface singularity; invariants

Articles in the same Issue

  1. Frontmatter
  2. Rings of differential operators on (k,s)-th Tjurina algebras of singularities
  3. Cokernels of random matrix products and flag Cohen–Lenstra heuristic
  4. Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
  5. The L p -L q compactness of commutators of oscillatory singular integrals
  6. Determination of a pair of newforms from the product of their twisted central values
  7. Metrical properties of exponentially growing partial quotients
  8. Nonlinear operations and factorizations on a class of affine modulation spaces
  9. On algebraic degrees of certain exponential sums over finite fields
  10. The ranks of (a,b)-Fibonacci sequences and congruences for certain partition functions and Ramanujan's mock theta functions
  11. Dynamics of radial threshold solutions for generalized energy-critical Hartree equation
  12. Modular representations of GL2(𝔽𝑞) using calculus
  13. Bounding the number of p'-degree characters from below
  14. Existence and multiplicity of non-radial sign-changing solutions for a semilinear elliptic equation in hyperbolic space
  15. Duality theorems for polyanalytic functions
  16. Lower bounds for the number of number fields with Galois group GL2(𝔽ℓ)
  17. Cylindrical ample divisors on Du Val del Pezzo surfaces
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