Context : Hadronic matter undergoes a deconfinement transition to quark matter at high temperature and/or high density .
It would be realized in collapsing cores of massive stars .

Aims : In the framework of MIT bag model , the ambiguities of the interaction are encapsulated in the bag constant .
Some progenitor stars that invoke the core collapses explode as supernovae , and other ones become black holes .
The fates of core collapses are investigated for various cases .

Methods : Equations of state including the hadron-quark phase transition are constructed for the cases of the bag constant B = 90 , 150 and 250 MeV fm ^ { -3 } .
To describe the mixed phase , the Gibbs condition is used .
Adopting the equations of state with different bag constants , the core collapse simulations are performed for the progenitor models with 15 and 40 M _ { \odot } .

Results : If the bag constant is small as B = 90 MeV fm ^ { -3 } , an interval between the bounce and black hole formation is shortened drastically for the model with 40 M _ { \odot } and the second bounce revives the shock wave leading to explosion for the model with 15 M _ { \odot } .

Conclusions :