Geodesic
Jet Bundles on Gorenstein Curves and Applications
Journal of Singularities, Tome 21 (2020), pp. 50-83

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The purpose of this expository paper is to present a catalogue of locally free replacements of the sheaves of principal parts for (families of) Gorenstein curves. In the smooth category, locally free sheaves of principal parts are better known as jet bundles, understood as those locally free sheaves whose transition functions reflect the transformation rules of the partial derivatives of a local section under a change of local coordinates. Being a natural globalisation of the fundamental notion of Taylor expansion of a function in a neighborhood of a point, jet bundles are ubiquitous in Mathematics. They proved powerful tools for the study of deformation theories within a wide variety of mathematical situations and have a number of purely algebraic incarnations: besides the aforementioned principal parts of a quasi-coherent sheaf we should mention, for instance, the theory of arc spaces on algebraic varieties, introduced by Nash to deal with resolutions of singular loci of singular varieties. 
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     author = {Letterio Gatto and Andrea T. Ricolfi},
     title = {Jet {Bundles} on {Gorenstein} {Curves} and {Applications}},
     journal = {Journal of Singularities},
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Letterio Gatto; Andrea T. Ricolfi. Jet Bundles on Gorenstein Curves and Applications. Journal of Singularities, Tome 21 (2020), pp. 50-83. doi: 10.5427/jsing.2020.21d

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