Arf Closure Relative to a Divisorial Valuation and Transversal Curves

1994 ◽  
Vol 116 (2) ◽  
pp. 377 ◽  
Author(s):  
Antonio Campillo ◽  
Julio Castellanos
Keyword(s):  
Divisorial Valuation

scholarly journals On the B-Semiampleness Conjecture

2019 ◽  
Vol Volume 3 ◽  
Author(s):  
Enrica Floris ◽  
Vladimir Lazić
Keyword(s):  
Canonical Bundle ◽  
Divisorial Valuation

The B-Semiampleness Conjecture of Prokhorov and Shokurov predicts that the moduli part in a canonical bundle formula is semiample on a birational modification. We prove that the restriction of the moduli part to any sufficiently high divisorial valuation is semiample, assuming the conjecture in lower dimensions. Comment: 26 pages

scholarly journals JET SCHEMES OF QUASI-ORDINARY SURFACE SINGULARITIES

2019 ◽  
pp. 1-88
Author(s):  
HELENA COBO ◽  
HUSSEIN MOURTADA
Keyword(s):  
Plane Curve ◽  
Topological Type ◽  
Weighted Graph ◽  
Singular Locus ◽  
Hypersurface Singularity ◽  
Log Canonical Threshold ◽  
Jet Schemes ◽  
Log Canonical ◽  
Irreducible Components ◽  
Divisorial Valuation

We describe the irreducible components of the jet schemes with origin in the singular locus of a two-dimensional quasi-ordinary hypersurface singularity. A weighted graph is associated with these components and with their embedding dimensions and their codimensions in the jet schemes of the ambient space. We prove that the data of this weighted graph is equivalent to the data of the topological type of the singularity. We also determine a component of the jet schemes (equivalent to a divisorial valuation on $\mathbb{A}^{3}$ ), that computes the log-canonical threshold of the singularity embedded in $\mathbb{A}^{3}$ . This provides us with pairs $X\subset \mathbb{A}^{3}$ whose log-canonical thresholds are not computed by monomial divisorial valuations. Note that for a pair $C\subset \mathbb{A}^{2}$ , where $C$ is a plane curve, the log-canonical threshold is always computed by a monomial divisorial valuation (in suitable coordinates of $\mathbb{A}^{2}$ ).

scholarly journals Approximating delta invariants in the sense of plt complements

2021 ◽  
Author(s):  
Chuyu Zhou
Keyword(s):  
Divisorial Valuation

AbstractWe show that delta invariant of a log Fano pair can be approximated by lc places of plt complements if it is no greater than one. Under the assumption that delta invariant (no greater than one) of a log Fano pair can be approximated by lc places of bounded plt complements, we show the existence of divisorial valuation computing delta invariant of this log Fano pair.

scholarly journals A divisorial valuation with irrational volume

2003 ◽  
Vol 262 (2) ◽  
pp. 413-423 ◽  
Author(s):  
Alex Küronya
Keyword(s):  
Divisorial Valuation
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