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This is a survey and research note on the modified Orlik conjecture derivedfrom the division theorem introduced in [2]. The division theorem is ageneralization of classical addition-deletion theorems for free arrangements.The division theorem can be regarded as a modified converse of the Orlik'sconjecture with a combinatorial condition, i.e., an arrangement is free if therestriction is free and the characteristic polynomial of the restrictiondivides that of an arrangement. In this article we recall, summarize, pose andre-formulate some of results and problems related to the division theorem basedon [2], and study the modified Orlik's conjecture with partial answers.

Restrictions of free arrangements and the division theorem