## Illinois Journal of Mathematics

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

S. P. Dutta

#### Abstract

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

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

Dates
First available in Project Euclid: 20 November 2009

https://projecteuclid.org/euclid.ijm/1258735324

Digital Object Identifier
doi:10.1215/ijm/1258735324

Mathematical Reviews number (MathSciNet)
MR2346186

Zentralblatt MATH identifier
1127.14016

#### Citation

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. https://projecteuclid.org/euclid.ijm/1258735324