Geodesic
Non-rational divisors over non-degenerate $cDV$-points
Sbornik. Mathematics, Tome 196 (2005) no. 7, pp. 1075-1088

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Suppose that $(X,o)$ is a 3-dimensional terminal singularity of type $cD$ or $cE$ defined in ${\mathbb C}^4$ by an equation that is non-degenerate with respect to its Newton diagram. We show that there exists at most one non-rational divisor $E$ over $(X,o)$ with discrepancy $a(E,X)=1$. We also describe all the blow-ups of the singularity $(X,o)$ with non-rational exceptional divisors of discrepancy 1. 
@article{SM_2005_196_7_a5,
     author = {D. A. Stepanov},
     title = {Non-rational divisors over non-degenerate $cDV$-points},
     journal = {Sbornik. Mathematics},
     pages = {1075--1088},
     publisher = {mathdoc},
     volume = {196},
     number = {7},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_7_a5/}
}
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D. A. Stepanov. Non-rational divisors over non-degenerate $cDV$-points. Sbornik. Mathematics, Tome 196 (2005) no. 7, pp. 1075-1088. http://geodesic.mathdoc.fr/item/SM_2005_196_7_a5/