▁Category : T ax onomy ▁articles ▁created ▁by ▁Pol bot <0x0A> </s> ▁The ▁women ' s ▁ 1 5 0 0 ▁metres ▁event ▁at ▁the ▁ 1 9 7 2 ▁European ▁Athletics ▁Ind oor ▁Championships ▁was ▁held ▁on ▁ 1 2 ▁March ▁in ▁Gren o ble . ▁ ▁Results ▁ ▁References ▁ ▁Category : 1 5 0 0 ▁metres ▁at ▁the ▁European ▁Athletics ▁Ind oor ▁Championships ▁ 1 5 0 0 <0x0A> </s> ▁In ▁mathematics , ▁specifically ▁in ▁the ▁study ▁of ▁vector ▁bund les ▁over ▁complex ▁K äh ler ▁manif olds , ▁the ▁Nak ano ▁van ishing ▁theorem , ▁sometimes ▁called ▁the ▁Ak iz uki – N ak ano ▁van ishing ▁theorem , ▁general izes ▁the ▁K od ai ra ▁van ishing ▁theorem . ▁Given ▁a ▁compact ▁complex ▁manifold ▁M ▁with ▁a ▁hol omorphic ▁line ▁bundle ▁F ▁over ▁M , ▁the ▁Nak ano ▁van ishing ▁theorem ▁provides ▁a ▁condition ▁on ▁when ▁the ▁coh om ology ▁groups ▁ ▁equal ▁zero . ▁Here , ▁ ▁denotes ▁the ▁she af ▁of ▁hol omorphic ▁( p , 0 )- forms ▁taking ▁values ▁on ▁F . ▁The ▁theorem ▁states ▁that , ▁if ▁the ▁first ▁Ch ern ▁class ▁of ▁F ▁is ▁negative , Al tern atively , ▁if ▁the ▁first ▁Ch ern ▁class ▁of ▁F ▁is ▁positive , ▁ ▁References ▁ ▁Original ▁publications ▁ ▁Second ary ▁sources ▁▁ ▁Category : The or ems ▁in ▁complex ▁geometry ▁Category : Top ological ▁methods ▁of ▁algebraic ▁geometry ▁Category : The or ems ▁in ▁algebraic ▁geometry <0x0A> </s> ▁Kl uster f uk ▁is