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- W4280493408 abstract "The Tjurina ideal of a germ of an holomorphic function $f$ is the ideal of $mathscr{O}_{mathbbm{C}^n,0}$ - the ring of those germs at $0inmathbbm{C}^n$ - generated by $f$ itself and by its partial derivatives. Here it is denoted by $T(f)$. The ideal $T(f)$ gives the structure of closed subscheme of $(mathbbm{C}^n,0)$ to the hypersurface singularity defined by $f$, being an object of central interest in Singularity Theory. In this note we introduce emph{$T$-fullness} and emph{$T$-dependence}, two easily verifiable properties for arbitrary ideals of germs of holomorphic functions. These two properties allow us to give necessary and sufficient conditions on an ideal $Isubset mathscr{O}_{mathbbm{C}^n,0}$, for the equation $I=T(f)$ to admit a solution $f$." @default.
- W4280493408 created "2022-05-22" @default.
- W4280493408 creator A5075252538 @default.
- W4280493408 date "2022-05-06" @default.
- W4280493408 modified "2023-09-27" @default.
- W4280493408 title "On Tjurina Ideals of Hypersurface Singularities" @default.
- W4280493408 doi "https://doi.org/10.48550/arxiv.2205.03527" @default.
- W4280493408 hasPublicationYear "2022" @default.
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