Illinois Journal of Mathematics

On efficient generation of pull-back of {$T\sb {\Bbb P\sp n}(-1)$}

S. P. Dutta

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Let $f: X\to \mathbb P^n$ be a proper map such that dimension of $f(X)\ge 2$. We address the following question: Is $\dim H^o(X,\,f^{\ast}(T_{\mathbb P^n}(-1)) = n + 1$? We provide an affirmative answer under standard mild restrictions on $X$. We also point out that this provides an affirmative answer to a similar question raised via regular alteration of a closed subvariety in a blow-up of a regular local ring at its closed point in the mixed characteristics.

Article information

Illinois J. Math., Volume 51, Number 1 (2007), 57-65.

First available in Project Euclid: 20 November 2009

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Primary: 13H15: Multiplicity theory and related topics [See also 14C17]
Secondary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]


Dutta, S. P. On efficient generation of pull-back of {$T\sb {\Bbb P\sp n}(-1)$}. Illinois J. Math. 51 (2007), no. 1, 57--65. doi:10.1215/ijm/1258735324.

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