## Illinois Journal of Mathematics

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

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

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1215/ijm/1258735324

**Mathematical Reviews number (MathSciNet)**

MR2346186

**Zentralblatt MATH identifier**

1127.14016

**Subjects**

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]

#### 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