# What I Got Wrong

I try to maintain a list of errors that, sadly, are in my printed work. Please  let me know if you know of an error that is not listed here.

#### (1) The Quantum Orbifold Cohomology of Weighted Projective Spaces (with Tom Coates, Hsian-Hua Tseng and Yuan-Pin Lee)

Corollary 6.2 and Corollary 1.9 of the journal version of the paper are incorrect. It remains a fundamental research challenge to prove the appropriate version of the quantum Lefschetz theorem for orbifolds (stacks).

#### (2) Conifold transitions and Mori theory (with Ivan Smith)

A critical error in Corollary 2 of the journal version of the paper (vanishing of the square of the first Chern class need not be preserved by the surgery) invalidates the proofs of both the main results. Ivan and I are grateful to Yi Jiang for pointing this out. A full erratum appears in:

Alessio Corti and Ivan Smith, Erratum to “Conifold transitions and Mori theory”, Math. Res. Lett. 23, No. 3, 2016, 733-734

#### (3) Singularities of linear systems and 3-fold birational geometry

The proof of Theorem 6.4 is wrong. The theorem states the birational rigidity of a general 3-fold complete intersection of a quadric and a cubic in $$\mathbb{P}^5$$. The original proof of this result, due to Aleksandr Pukhlikov, is correct to my knowledge. The mistake is in lines 5-6 on page 306, where the text states, incorrectly, that “we may also assume that the singularity […] is analytically equivalent to a cone over 4 general points in $$\mathbb{P}^2$$.” I am very grateful to Constantin Shramov for pointing this out to me. I would love to see my attempt here resurrected somehow. Let me know if you want to work on it: I will do all I can to help.