Nyob rau hauv lej, birational geometry yog ib thaj tsam ntawm algebraic geometry uas lub hom phiaj yog los txiav txim siab thaum twg ob hom algebraic yog isomorphic sab nraum cov subsets qis dua.
Dab tsi yog birational?
birationalaadjective. Piav txog qhov muaj nuj nqis geometric uas muaj qhov sib txawv ntawm qhov sib txawv.
daim ntawv qhia birational yog dab tsi?
Ib daim ntawv qhia kev sib txawv ntawm X rau Y yog a daim ntawv qhia kev sib tw f: X ⇢ Y xws li tias muaj daim ntawv qhia kev sib tw Y ⇢ X inverse mus f. Ib daim ntawv qhia birational induces ib isomorphism los ntawm ib tug tsis muaj npe qhib subset ntawm X mus rau ib tug nonnempty qhib subset ntawm Y. Nyob rau hauv cov ntaub ntawv no, X thiab Y yog hais tias yog birational, los yog birationally sib npaug.
Dab tsi yog algebraic geometry siv rau?
Algebraic geometry tam sim no pom cov ntawv thov hauv statistics, tswj txoj kev xav, neeg hlau, yuam kev-kho cov lej, phylogenetics thiab geometric qauv. Kuj tseem muaj kev sib txuas rau txoj hlua txoj kev xav, kev ua si txoj kev xav, cov duab sib txuam, solitons thiab integer programming.
Vim li cas algebraic geometry thiaj li nrov?
Yog li, cov lej kawm txog algebraic geometry vim nws yog lub hauv paus ntawm ntau yam kev kawm, ua tus choj ntawm seemingly txawv kev qhuab qhia: los ntawm geometry thiab topology mus rau txoj kev tsom xam thiab lej txoj kev xav..
