1. The tenant continues in possession of any portion of the premises after the expiration of his term, without the permission of the landlord or, in a case where a new lessee is entitled to possession, without the permission of the new lessee. Acceptance of rent after commencement of the special proceeding upon this ground shall not terminate such proceeding nor effect any award of possession to the landlord or to the new lessee, as the case may be. A proceeding seeking to recover possession of real property by reason of the termination of the term fixed in the lease pursuant to a provision contained therein giving the landlord the right to terminate the time fixed for occupancy under such agreement if he deem the tenant objectionable, shall not be maintainable unless the landlord shall by competent evidence establish to the satisfaction of the court that the tenant is objectionable.2. The tenant has defaulted in the payment of rent, pursuant to the agreement under which the premises are held, and a written demand of the rent has been made with at least fourteen days' notice requiring, in the alternative, the payment of the rent, or the possession of the premises, has been served upon him as prescribed in section seven hundred thirty-five of this article. Any person succeeding to the landlord's interest in the premises may proceed under this subdivision for rent due his predecessor in interest if he has a right thereto. Where a tenant dies during the term of the lease and rent due has not been paid and the apartment is occupied by a person with a claim to possession, a proceeding may be commenced naming the occupants of the apartment seeking a possessory judgment only as against the estate. Entry of such a judgment shall be without prejudice to the possessory claims of the occupants, and any warrant issued shall not be effective as against the occupants.3. The tenant, in a city defaults in the payment, for sixty days after the same shall be payable, of any taxes or assessments levied on the premises which he has agreed in writing to pay pursuant to the agreement under which the premises are held, and a demand for payment has been made, or at least three days' notice in writing, requiring in the alternative the payment thereof and of any interest and penalty thereon, or the possession of the premises, has been served upon him, as prescribed in section 735. An acceptance of any rent shall not be construed as a waiver of the agreement to pay taxes or assessments.4. The tenant, under a lease for a term of three years or less, has during the term taken the benefit of an insolvency statute or has been adjudicated a bankrupt.5. The premises, or any part thereof, are used or occupied as a bawdy-house, or house or place of assignation for lewd persons, or for purposes of prostitution, or for any illegal trade or manufacture, or other illegal business.6. The tenant, in a city having a population of one million or more, removes the batteries or otherwise disconnects or makes inoperable an installed smoke or fire detector which the tenant has not requested be moved from its location so as not to interfere with the reasonable use of kitchen facilities provided that the court, upon complaint thereof, has previously issued an order of violation of the provisions heretofore stated and, subsequent to the thirtieth day after service of such order upon the tenant, an official inspection report by the appropriate department of housing preservation and development is presented, in writing, indicating non-compliance herewith; provided further, that the tenant shall have the additional ten day period to cure such violation in accordance with the provisions of subdivision four of section seven hundred fifty-three of this chapter.