We construct an algebraic almost closed 1-form with zero scheme not expressible (even locally) as the critical locus of a holomorphic function on a non-singular variety. The result answers a question of Behrend-Fantechi. We correct here an error in our paper (D. Maulik, R Pandharipande and R. P. Thomas, Curves on K3 surfaces and modular forms, J. Topol. 3 (2010) 937-996. arXiv:1001.2719v3), where an incorrect construction with the same claimed properties was propose
