
samanya bindu

beejganitiya jyaamiti mein, ack beejganitiya vividhata "x" kaa ack samanya bindu "p", motey taur parr, ack bindu haye jiss parr sabhi samanya guna sahee hain, ack samanya guna ack guna haye joe lagbhag harr bindu key liye sahee haye.
shaastriya beejganitiya jyaamiti mein, ayam "d" kii ack abhisoochak yaa prakshepaatmak beejganitiya vividhata kaa ack samanya bindu aisaa bindu haye kii isake nirdeshankon dwara utpann kshetra mein vividhata key samikaranon key gunank dwara utpann kshetra parr paar degree "d" hoti haye.
yojana siddhant mein, ack abhinn kshetra key varnakram mein ack advitiya samanya bindu hotaa haye, joe shoonya aadarsh haye. choonki zariski topology key liye iss bindu kaa samaapan poore spectrum key roop mein hotaa haye, isaliye paribhasha koo samanya topology taka badhaaya gayaa haye, jahaan ack topological sthaan "x" kaa ack samanya bindu ack bindu haye jiska samaapan "x" haye.
paribhasha aur prerana.
sthalshastriya sthaan "x" kaa ack samanya bindu ack bindu "p" haye jiska puuraa samaapan "x" haye, yaani ack bindu joe "x" mein ghanaa haye.
shabdawali ack beejganitiya samooh kii upa-kismon key samooh parr zariski topology key mamle seey utpann hoti haih beejganitiya sett irreducible haye (yaani, yeh dou uchit beejganitiya upa-samoohon kaa sangh naheen haye) yadi aur kewal tabhi jaba upa-kismon key topological sthaan mein ack samanya bindu hoe.
itihas.
andrey weill key moolbhoot drishtikon mein, joe unaki "beejganitiya jyaamiti kii neenv" mein vikasit huaa, samanya binduon ney ack mahatvapurna bhoomika nibhai, lekin ack alag tareeke seey sambhala gayaa. ack beejganitiya vividhata key liye "v" ack kshetra "k" parr, "v" key "samanya bindu" ack saarvbhaumik kshetra ω mein maan lene vaale "v" key binduon kaa ack puuraa varg thaa, ack beejganitiya roop seey bund kshetra jisamen "k" hotaa haye, lekin taaja anishchit kii ack anant aapoorti bhee hoti haye. yeh drishtikon "v" ("k"-zariski topology, arthaat) key topology key saath seedhe nipatane kii aavashyakta key binaa kaam kartaa haye, kyonki visheshagyataon parr sabhi kshetra star parr charcha kii jaa sakati haye (jaisa kii beejganitiya jyaamiti key mulyankan siddhant drishtikon mein, 1930 key dashak mein lokpriya).
yeh samaan roop seey samanya binduon key ack vishal sangrah kii keemat parr thaa. dwiteeya vishva yuddh key thheek baad saao paulo mein wheels key ack sahayogi auskar zariski ney hamesha jore dekar kahaa kii samanya bindu advitiya honey chaahiye. (ise shirshavigyaani key shabdon mein vaapas rakhaa jaa sakata haih wheel kaa vichaar ack kolmogorov sthaan dene mein whiffle rahata haye aur zariski kolmogorov bhagfal key sandarbh mein sochata haye.)
1950 key dashak key teji seey moolbhoot parivartanon mein wheel kaa drishtikon aprachalit hoe gayaa. yojana siddhant mein, halanki, 1957 seey, samanya bindu laut aaeh iss baar "aeye laa zariski". udaaharan key liye "r" key liye ack asatat mulyankan valay "," vishisht "(" r ") mein dou bindu hotey hain, ack samanya bindu (pradhaan aadarsh {0} seey aataa haye) aur ack bund bindu yaa vishisht adhikatam aadarsh seey aaney vaalaa vishesh bindu. vishishtata" ("aar") key roop mein rupankan key liye, vishesh bindu key oopar fiber vishesh fiber haye, udaaharan key liye reduction modulo pee, monodromy siddhant aur apakshay key baare mein anya siddhanton mein ack mahatvapurna avadharana haye. samaan roop seey, samanya fiber samanya bindu key oopar kaa fiber haye. apakshay kii jyaamiti kaafee hudd taka samanya seey vishesh tantuon taka jaane key baare mein haye, yaa dusare shabdon mein maapdandon kii visheshagyata mamalon koo kaise prabhaavit karati haye. (ack asatat mulyankan ring key liye prashn mein topological sthaan topologists kaa sairpinsky sthaan haye. anya sthaaniya valayon mein advitiya samanya aur vishesh bindu hotey hain, lekin ack adhik jatil varnakram hotaa haye, kyonki way samanya aayamon kaa pratinidhitva karate hain. inn uddeshyon key liye asatat mulyankan mamla bahut hudd taka jatil ikai disk kii tarah haye.)

