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Upper bound of discrepancies of divisors computing minimal log discrepancies on surfaces.

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Τίτλος: Upper bound of discrepancies of divisors computing minimal log discrepancies on surfaces.
Συγγραφείς: Chen, Bingyi1 (AUTHOR) chenby16@tsinghua.org.cn
Πηγή: Journal of Algebra. Aug2026, Vol. 700, p69-86. 18p.
Θεματικοί όροι: *Algebraic geometry, *Mathematical singularities, *Geometric surfaces
Περίληψη: Fix a subset I ⊆ R > 0 such that γ : = inf ⁡ { ∑ i n i b i − 1 > 0 | n i ∈ Z ≥ 0 , b i ∈ I } > 0. We give an explicit upper bound ℓ (γ) ∈ O (1 / γ 2) as γ → 0 , such that for any smooth surface A of arbitrary characteristic with a closed point 0 and an R -ideal a with exponents in I , there always exists a prime divisor E over A computing the minimal log discrepancy of (A , a) at 0 and with its log discrepancy k E + 1 ≤ ℓ (γ). Some examples indicate that our bound is optimal. [ABSTRACT FROM AUTHOR]
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  Data: Fix a subset I ⊆ R > 0 such that γ : = inf ⁡ { ∑ i n i b i − 1 > 0 | n i ∈ Z ≥ 0 , b i ∈ I } > 0. We give an explicit upper bound ℓ (γ) ∈ O (1 / γ 2) as γ → 0 , such that for any smooth surface A of arbitrary characteristic with a closed point 0 and an R -ideal a with exponents in I , there always exists a prime divisor E over A computing the minimal log discrepancy of (A , a) at 0 and with its log discrepancy k E + 1 ≤ ℓ (γ). Some examples indicate that our bound is optimal. [ABSTRACT FROM AUTHOR]
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        Value: 10.1016/j.jalgebra.2026.04.003
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      – Code: eng
        Text: English
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        PageCount: 18
        StartPage: 69
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      – SubjectFull: Algebraic geometry
        Type: general
      – SubjectFull: Mathematical singularities
        Type: general
      – SubjectFull: Geometric surfaces
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      – TitleFull: Upper bound of discrepancies of divisors computing minimal log discrepancies on surfaces.
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              Text: Aug2026
              Type: published
              Y: 2026
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