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Logarithmic sheaves of complete intersections

Abstract : We define logarithmic tangent sheaves associated with complete intersections in connection with Jacobian syzygies and distributions. We analyse the notions of local freeness, freeness and stability of these sheaves. We carry out a complete study of logarithmic sheaves associated with pencils of quadrics and compute their projective dimension from the classical invariants such as the Segre symbol and new invariants (splitting type and degree vector) designed for the classification of irregular pencils. This leads to a complete classification of free (equivalently, locally free) pencils of quadrics. Finally we produce examples of locally free, non free pencils of surfaces in P3 of any degree k at least 3, answering (in the negative) a question of Calvo-Andrade, Cerveau, Giraldo and Lins Neto about codimension foliations on P3 .
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03271244
Contributor : Daniele FAENZI Connect in order to contact the contributor
Submitted on : Friday, June 25, 2021 - 2:57:55 PM
Last modification on : Friday, August 5, 2022 - 11:52:05 AM
Long-term archiving on: : Sunday, September 26, 2021 - 10:17:13 PM

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logsheaves_arxiv.v1.pdf
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  • HAL Id : hal-03271244, version 1
  • ARXIV : 2106.14453

Citation

Daniele Faenzi, Marcos Jardim, Jean Vallès. Logarithmic sheaves of complete intersections. 2021. ⟨hal-03271244⟩

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