Dependence of Lyubeznik numbers of cones of projective schemes on projective embeddings

Thomas Reichelt ^[2] ; Morihiko Saito ^[3] ; Uli Walther ^[1]
1. [1] Purdue University
  
  Purdue University
  
  Township of Wabash, Estados Unidos
2. [2] Universität Heidelberg, Alemania
3. [3] RIMS Kyoto University, Japón
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Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 1, 2021
Idioma: inglés
DOI: 10.1007/s00029-020-00612-3
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Resumen
- We construct complex projective schemes with Lyubeznik numbers of their cones depending on the choices of projective embeddings. This answers a question of G. Lyubeznik in the characteristic 0 case. It contrasts with a theorem of W. Zhang in the positive characteristic case where the Frobenius endomorphism is used. Reducibility of schemes is essential in our argument. B. Wang recently constructed examples of irreducible projective schemes (which are not normal) from our examples of reducible ones. So the question is still open in the normal singular case.