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4. Definitions of higher singularities and related invariants


    1. Add remark

      Problem 4.1.

      [Shend Zhjeqi] Is there an analytic characterization of the minimal exponent in the lci case?


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          Problem 4.2.

          [Alexandra Viktorova] What is the correct notion of higher DB singularities in the symplectic case?


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              Problem 4.3.

              [Radu Laza and Sándor Kovács] What is the a definition of m-Du Bois singularities satisfying:
              1. 0-Du Bois = Du Bois;
              2. m-Du Bois $\Rightarrow$ (m-1)-Du Bois;
              3. $R^i f_* \Omega_{X/S}^m$ is locally free, and compatible with base change for any flat family $f: X \rightarrow S$ with pre-m-Du Bois fibers.
                1. Remark. [Bradley Dirks] Can we define it if $\mathbb{Q}_X[\dim X]$ is perverse?


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                      Problem 4.4.

                      [Brad Dirks] Is there a notion of minimal exponent in the non-lci case related to higher singularities? This requires p-Du Bois $\Rightarrow$ (p-1)-rational.

                      Is there an invariant characterizing rational singularities?


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                          Problem 4.5.

                          Is there a good notion of a relative Du Bois complex?

                              Cite this as: AimPL: Higher Du Bois and higher rational singularities, available at http://aimpl.org/higherdubois.