On the homogeneous ideal of a projective nonsingular toric variety

TL;DR

This paper investigates the algebraic structure of the homogeneous ideal associated with a smooth projective toric variety, aiming to deepen understanding of its geometric and combinatorial properties.

Contribution

It attempts to analyze the homogeneous ideal of nonsingular projective toric varieties, although the main proof contains a critical error.

Findings

The initial proof was invalid due to a mistake in divisor calculation.

The correction of the divisor calculation affects the validity of the main argument.

The paper's conclusions are currently uncertain pending correction of the proof.

Abstract

Reason for withdrawal: There is a serious mistake in the calculation of the divisor of the rational section used in the proof of Prop. 2.2.1., and with the correct value the argument does not work.