Geodesic
The Delta Invariant and Fiberwise Normalization for Families of isolated Non-Normal Singularities
Journal of Singularities, Tome 25 (2022), pp. 173-196

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We prove the semicontinuity of the delta invariant in a family of schemes or analytic varieties with finitely many (not necessarily reduced) isolated non-normal singularities, in particular for families of generically reduced curves. We define and use a modified delta invariant for isolated non-normal singularities of any dimension that takes care of embedded points. Our results generalize results by Teissier and Chiang-Hsieh--Lipman for families of reduced curve singularities. The base ring for our families can be an arbitrary PID such that our semicontinuity result provides possible improvements for algorithms to compute the genus of a curve.
DOI : 10.5427/jsing.2022.25j
Classification : 13B22, 13B40, 14B05, 14B07 
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     author = {Gert-Martin Greuel and Gerhard Pfister},
     title = {The {Delta} {Invariant} and {Fiberwise} {Normalization} for {Families} of isolated {Non-Normal} {Singularities}},
     journal = {Journal of Singularities},
     pages = {173--196},
     publisher = {mathdoc},
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     year = {2022},
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Gert-Martin Greuel; Gerhard Pfister. The Delta Invariant and Fiberwise Normalization for Families of isolated Non-Normal Singularities. Journal of Singularities, Tome 25 (2022), pp. 173-196. doi: 10.5427/jsing.2022.25j

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