Inversion of Adjunction for the minimal exponent
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e92

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that the minimal exponent for local complete intersections satisfies an Inversion-of-Adjunction property. As a result, we also obtain the Inversion of Adjunction for higher Du Bois and higher rational singularities for local complete intersections.
Chen, Qianyu. Inversion of Adjunction for the minimal exponent. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e92. doi: 10.1017/fms.2025.45
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[AK] Acuna, R and Kerr, M., ‘Hodge adjacency conditions for singularities’, Talk at AIM workshop: Higher Du Bois and Higher Rational Singularities. Google Scholar

[BMS06] Budur, N., Mustaţă, M. and Saito, M., ‘Bernstein-Sato polynomials of arbitrary varieties’, Compos. Math. 142(3) (2006), 779–797.10.1112/S0010437X06002193 Google Scholar | DOI

[CD23] Chen, Q. and Dirks, B., ‘On -filtration, Hodge filtration and Fourier transform’, Selecta Math. 29(4) (2023), 50.10.1007/s00029-023-00850-1 Google Scholar | DOI

[CDM24a] Chen, Q., Dirks, B. and Mustaţă, M., ‘The minimal exponent and -rationality for local complete intersections’, J. Éc. polytech. Math. 11 (2024), 849–873.10.5802/jep.267 Google Scholar | DOI

[CDM24b] Chen, Q., Dirks, B. and Mustaţă, M., ‘The minimal exponent of cones over smooth complete intersection projective varieties’, to appear in Revue Roumaine Math. Pures Appl., volume in memory of Lucian Bădescu (2024). Google Scholar

[CDMO24] Chen, Q., Dirks, B., Mustaţă, M. and Olano, S., ‘-filtrations and minimal exponents for local complete intersections’, J . Reine Angew. Math. 811 (2024), 219–256. Google Scholar

[CDO24] Chen, Q., Dirks, B. and Olano, S., ‘Restrictions of mixed Hodge modules using generalized -filtrations’, Preprint, 2024, . Google Scholar | arXiv

[CM25] Chen, Q. and Mustaţă, M., ‘A birational description of the minimal exponent’, Preprint, 2023, . Google Scholar | arXiv

[OD15] Das, Omprakash, ‘On strongly -regular Inversion of Adjunction’, J. Algebra 434 (2015), 207–226.10.1016/j.jalgebra.2015.03.025 Google Scholar | DOI

[Del06] Deligne, P., Equations différentielles à points singuliers réguliers, Lect. Notes in Math., vol. 163 (Springer Berlin, Heidelberg, 1970).10.1007/BFb0061194 Google Scholar | DOI

[DB81] Du Bois, P., ‘Complexe de de Rham filtré d’une variété singulière’, Bull. Soc. Math. France 109 (1981), 41–81 (French).10.24033/bsmf.1932 Google Scholar | DOI

[Dir23] Dirks, B., ‘Some applications of microlocalization for local complete intersection subvarieties’, Preprint, 2023, . Google Scholar | arXiv

[DM23] Dirks, B. and Mustaţă, M., ‘Minimal exponents of hyperplane sections: a conjecture of Teissier’, J. Eur. Math. Soc. 25(12) (2023), 4503–4528. Google Scholar

[FL22] Friedman, R. and Laza, R., ‘Deformations of singular Fano and Calabi-Yau varieties’, to appear in J. Differential Geom. (2022). Google Scholar

[FL24a] Friedman, R. and Laza, R., ‘Higher Du Bois and higher rational singularities’, Duke Math. J. 173(10) (2024), 1839–1881. With an appendix by M. Saito.10.1215/00127094-2023-0051 Google Scholar | DOI

[FL24b] Friedman, R. and Laza, R., ‘The higher Du Bois and higher rational properties for isolated singularities’, J. Algebraic Geom. 33(3) (2024), 493–520.10.1090/jag/824 Google Scholar | DOI

[Hac14] Hacon, C., ‘On the log canonical Inversion of Adjunction’, Proc. Edinb. Math. Soc. 57(1) (2014), 139143.10.1017/S0013091513000837 Google Scholar | DOI

[HTT07] Hotta, R., Tanisaki, K. and Tsuchihashi, T., -modules, Perverse Sheaves, and Representation Theory, Progr. Math., vol. 236, (Birkhäuser, Boston, 2008). Translated from the 1995 Japaneseedition by Takeuchi.10.1007/978-0-8176-4523-6 Google Scholar | DOI

[JKSY22] Jung, S.-J., Kim, I.-K., Saito, M. and Yoon, Y., ‘Higher Du Bois singularities of hypersurfaces’, Proc. Lond. Math. Soc. 125(3) (2022), 543–567.10.1112/plms.12464 Google Scholar | DOI

[Kol97] Kollár, J., ‘Singularities of pairs’,in Algebraic Geometry—Santa Cruz 1995 (Proc. Sympos. Pure Math.) vol. 62 (Amer. Math. Soc., Providence, RI, 1997), 221–287.10.1090/pspum/062.1/1492525 Google Scholar | DOI

[Kol13] Kollár, J., Singularities of the Minimal Model Program, vol. 200 (Cambridge University Press, 2013).10.1017/CBO9781139547895 Google Scholar | DOI

[Kas83] Kashiwara, M., ‘Vanishing cycle sheaves and holonomic systems of differential equations’, Algebraic Geometry (Tokyo/Kyoto, 1982) (Lecture Notes in Math.) vol. 1016 (Springer, Berlin, 1983), 134–142.10.1007/BFb0099962 Google Scholar | DOI

[KS16] Kovács, S. and Schwede, K., ‘Inversion of Adjunction for rational and Du Bois pairs’, Algebra & Number Theory 10(5) (2016), 969–1000.10.2140/ant.2016.10.969 Google Scholar | DOI

[Kaw07] Kawakita, M., ‘Inversion of Adjunction on log canonicity’, Invent. Math. 167 (2007), 129–133.10.1007/s00222-006-0008-z Google Scholar | DOI

[Lic89] Lichtin, B., ‘Poles of and roots of the -function’, Ark. Mat. 27(2) (1989), 283–304.10.1007/BF02386377 Google Scholar | DOI

[Loe84] Loeser, F., ‘Exposant d’Arnold et sections planes’, C. R. Acad. Sci. Paris Sér. I Math., 1984, 485–488. Google Scholar

[Mal83] Malgrange, B., Polynômes de Bernstein-Sato et cohomologie évanescente, Analyse et topologie sur les espaces singuliers, II, III (Luminy, 1981) (Astérisque) vol. 101–102 (Soc. Math. France, Paris, 1983), 243–267. Google Scholar

[MOPW23] Mustaţă, M., Olano, S., Popa, M. and Witaszek, J., ‘The Du Bois complex of a hypersurface and the minimal exponent’, Duke Math. J. 172(7) (2023), 1411–1436.10.1215/00127094-2022-0074 Google Scholar | DOI

[MP19a] Mustaţă, M. and Popa, M., ‘Hodge ideals’, Mem. Amer. Math. Soc. 262(1278) (2019), v+80. Google Scholar

[MP19b] Mustaţă, M. and Popa, M., ‘Hodge ideals for -divisors: birational approach’, J. Éc. polytech. Math. 6 (2019), 283–328. 10.5802/jep.94 10.5802/jep.94 Google Scholar | DOI

[MP22a] Mustaţă, M. and Popa, M., ‘Hodge filtration on local cohomology, Du Bois complex and local cohomological dimension’, Forum Math. Pi 10 (2022), Paper No. e22, 58.10.1017/fmp.2022.15 Google Scholar | DOI

[MP22b] Mustaţă, M. and Popa, M., ‘On -rational and -Du Bois local complete intersections’, to appear in Algebraic Geometry (2022). Google Scholar

[MSS17] Ma, L., Schwede, K. and Shimomoto, K., ‘Local cohomology of Du Bois singularities and applications to families’, Compos. Math. 153(10) (2017), 2147–2170.10.1112/S0010437X17007321 Google Scholar | DOI

[Par23] Park, S. G., ‘Du Bois complex and extension of forms beyond rational singularities’, Preprint, 2023, . Google Scholar | arXiv

[PS08] Peters, C. and Steenbrink, J., Mixed Hodge Structures (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]) vol. 52 (Springer-Verlag, Berlin, 2008). Google Scholar

[PST23] Polstra, T., Simpson, A. and Tucker, K., ‘On -pure Inversion of Adjunction’, Preprint, 2023, . Google Scholar | arXiv

[Sai88] Saito, M., ‘Modules de Hodge polarisables’, Publ. Res. Inst. Math. Sci. 24 (1988), 849–995.10.2977/prims/1195173930 Google Scholar | DOI

[Sai90] Saito, M., ‘Mixed Hodge modules’, Publ. Res. Inst. Math. Sci. 26 (1990), 221–333.10.2977/prims/1195171082 Google Scholar | DOI

[Sai94] Saito, M., ‘On microlocal -function’, Bull. Soc. Math. France 122 (1994), 183–184. Google Scholar

[Sai00] Saito, M., ‘Mixed Hodge complexes on algebraic varieties’, Math. Ann. 316 (2000), 283–331.10.1007/s002080050014 Google Scholar | DOI

[Sai16] Saito, M., ‘Hodge ideals and microlocal -filtration’, Preprint, 2016, . Google Scholar | arXiv

[Sch07] Schwede, K., ‘A simple characterization of Du Bois singularities’, Compos. Math. 143(4) (2007), 813–828.10.1112/S0010437X07003004 Google Scholar | DOI

[SVV23] Shen, W., Venkatesh, S. and Vo, A., ‘On -Du Bois and -rational singularities’, Preprint, 2023, . Google Scholar | arXiv

[Ste85] Steenbrink, J. H. M., ‘Semicontinuity of the singularity spectrum’, Invent. Math. 79(3) (1985), 557–565.10.1007/BF01388523 Google Scholar | DOI

[Var82] Varchenko, A. N., ‘The complex singularity index does not change along the stratum ’, Funktsional. Anal. i Prilozhen. 16(1) (1982), 1–12, 96.10.1007/BF01081801 Google Scholar | DOI

[Wei20] Wei, C., ‘Logarithmic comparison with smooth boundary divisor in mixed Hodge modules’, Michigan Math. J. 69(1) (2020), 201–223.10.1307/mmj/1574326883 Google Scholar | DOI

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