Papers and preprints

Published/Accepted Papers

1. On log surfaces.
   O. Fujino, H. Tanaka,
   Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), no. 8, 109-114.
   
   
2. Minimal models and abundance for positive characteristic log surfaces.
   H. Tanaka,
   Nagoya Math. J. 216 (2014), 1-70.
   
   
3. On rational connectedness of globally F-regular threefolds.
   Y. Gongyo, Z. Li, Z. Patakfalvi, K. Schwede, H. Tanaka, R. Zong
   Adv. Math. 280 (2015), 47-78.
   
   
4. The trace map of Frobenius and extending sections for threefolds.
   H. Tanaka,
   Michigan Math. J. 64 (2015), no. 2, 227-261.
   
   
5. The X-method for klt surfaces in positive characteristic.
   H. Tanaka,
   J. Algebraic Geom. 24 (2015), no. 4, 605-628.
   
   
6. On base point freeness in positive characteristic.
   P. Cascini, H. Tanaka, C. Xu,
   Ann. Sci. Éc. Norm. Supér. (4) 48 (2015), no. 5, 1239-1272.
   
   
7. Abundance theorem for semi log canonical surfaces in positive characteristic.
   H. Tanaka,
   Osaka J. Math. 53 (2016), no. 2, 535-566.
   
   
8. A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf.
   A. Sannai, H. Tanaka,
   Math. Ann. 366 (2016), no. 3-4, 1067-1087.
   
   
9. On log del Pezzo surfaces in large characteristic.
   P. Cascini, H. Tanaka, J. Witaszek,
   Compos. Math. 153 (2017), no. 4, 820-850.
   
   
10. Semiample perturbations for log canonical varieties over an F-finite field containing an infinite perfect field.
    H. Tanaka,
    Internat. J. Math. 28 (2017), no. 5, 1750030, 13 pp.
    
    
11. Smooth rational surfaces violating Kawamata-Viehweg vanishing.
    P. Cascini, H. Tanaka,
    Eur. J. Math. 4 (2018), no. 1, 162-176.
    
    
12. Minimal model program for excellent surfaces.
    H. Tanaka,
    Ann. Inst. Fourier (Grenoble) 68 (2018), no. 1, 345-376.
    
    
13. Klt del Pezzo surfaces which are not globally F-split.
    P. Cascini, H. Tanaka, J. Witaszek,
    Int. Math. Res. Not. IMRN 2018, no. 7, 2135-2155.
    
    
14. Zariskian adic spaces.
    H. Tanaka,
    Kodai Math. J. 41 (2018), no. 3, 652-695.
    
    
15. Behavior of canonical divisors under purely inseparable base changes.
    H. Tanaka,
    J. Reine Angew. Math. 744 (2018), 237-264.
    
    
16. Infinite dimensional excellent rings.
    H. Tanaka,
    Comm. Algebra 47 (2019), no. 2, 482-489.
    
    
17. Purely log terminal threefolds with non-normal centres in characteristic two.
    P. Cascini, H. Tanaka,
    Amer. J. Math. 141 (2019), no. 4, 941-979.
    
    
18. Infinitely generated symbolic Rees algebras over finite fields.
    A. Sannai, H. Tanaka,
    Algebra Number Theory 13 (2019), no. 8, 1879-1891.
    
    
19. Rational points on log Fano threefolds over a finite field.
    Y. Gongyo, Y. Nakamura, H. Tanaka,
    J. Eur. Math. Soc. (JEMS) 21 (2019), no. 12, 3759-3795.
    
    
20. A Witt Nadel vanishing theorem for threefolds.
    Y. Nakamura, H. Tanaka,
    Compos. Math. 156 (2020), no. 3, 435-475.
    
    
21. Abundance theorem for surfaces over imperfect fields.
    H. Tanaka,
    Math. Z. 295 (2020), no. 1-2, 595-622.
    
    
22. Relative semi-ampleness in positive characteristic.
    P. Cascini, H. Tanaka,
    Proc. Lond. Math. Soc. (3) 121 (2020), no. 3, 617-655.
    
    
23. Pathologies on Mori fibre spaces in positive characteristic.
    H. Tanaka,
    Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 20 (2020), no. 3, 1113-1134.
    
    
24. Minimal model program for log canonical threefolds in positive characteristic.
    K. Hashizume, Y. Nakamura, H. Tanaka,
    Math. Res. Lett. 27 (2020), no. 4, 1003-1054.
    
    
25. Invariants of algebraic varieties over imperfect fields.
    H. Tanaka,
    Tohoku Math. J. (2) 73 (2021), no. 4, 471–538.
    
    
26. On p-power freeness in positive characteristic.
    H. Tanaka,
    Math. Nachr. 294 (2021), no. 10, 1968–1976.
    
    
27. Vanishing theorems of Kodaira type for Witt canonical sheaves.
    H. Tanaka,
    Selecta Math. (N.S.) 28 (2022), no. 1, Paper No. 12, 50 pp.
    
    
28. On del Pezzo fibrations in positive characteristic.
    F. Bernasconi, H. Tanaka,
    J. Inst. Math. Jussieu 21 (2022), no. 1, 197–239.
    
    
29. Bertini theorems admitting base changes.
    H. Tanaka,
    J. Algebra 644 (2024), 64–125.
    
    

Preprints

1. Boundedness of regular del Pezzo surfaces over imperfect fields.
2. Quasi-F-splittings in birational geometry (with T. Kawakami, T. Takamatsu, J. Witaszek, F. Yobuko, S. Yoshikawa).
3. Quasi-F-splittings in birational geometry II (with T. Kawakami, T. Takamatsu, J. Witaszek, F. Yobuko, S. Yoshikawa).
4. Kawamata-Viehweg vanishing for toric varieties.
5. Fano threefolds in positive characteristic I.
6. Fano threefolds in positive characteristic II.
7. Fano threefolds in positive characteristic III (with Masaya Asai).
8. Fano threefolds in positive characteristic IV.
9. Discriminant divisors for conic bundles.
10. Elliptic sigularities and threefold flops in positive characteristic.
11. Global F-regularity for weak del Pezzo surfaces (with Tatsuro Kawakami).
12. Smooth del Pezzo varieties are quasi-F-split (with Tatsuro Kawakami).
13. Vanishing theorems for Fano threefolds in positive characteristic (with Tatsuro Kawakami).
14. Quasi-F^e-splittings and quasi-F-regularity (with Jakub Witaszek, Fuetaro Yobuko).