id sid tid token lemma pos gb19f478f3j 1 1 this this DET gb19f478f3j 1 2 paper paper NOUN gb19f478f3j 1 3 proves prove VERB gb19f478f3j 1 4 geometric geometric ADJ gb19f478f3j 1 5 manin manin NOUN gb19f478f3j 1 6 's 's PART gb19f478f3j 1 7 conjecture conjecture NOUN gb19f478f3j 1 8 for for ADP gb19f478f3j 1 9 smooth smooth ADJ gb19f478f3j 1 10 fano fano PROPN gb19f478f3j 1 11 threefolds threefold NOUN gb19f478f3j 1 12 over over ADP gb19f478f3j 1 13 the the DET gb19f478f3j 1 14 complex complex ADJ gb19f478f3j 1 15 numbers number NOUN gb19f478f3j 1 16 and and CCONJ gb19f478f3j 1 17 of of ADP gb19f478f3j 1 18 picard picard NOUN gb19f478f3j 1 19 rank rank NOUN gb19f478f3j 1 20 at at ADV gb19f478f3j 1 21 least least ADJ gb19f478f3j 1 22 two two NUM gb19f478f3j 1 23 . . PUNCT gb19f478f3j 2 1 geometric geometric ADJ gb19f478f3j 2 2 manin manin PROPN gb19f478f3j 2 3 's 's PART gb19f478f3j 2 4 conjecture conjecture NOUN gb19f478f3j 2 5 translates translate VERB gb19f478f3j 2 6 batyrev batyrev PROPN gb19f478f3j 2 7 's 's PART gb19f478f3j 2 8 heuristic heuristic NOUN gb19f478f3j 2 9 for for ADP gb19f478f3j 2 10 manin manin PROPN gb19f478f3j 2 11 's 's PART gb19f478f3j 2 12 conjecture conjecture NOUN gb19f478f3j 2 13 to to ADP gb19f478f3j 2 14 a a DET gb19f478f3j 2 15 statement statement NOUN gb19f478f3j 2 16 about about ADP gb19f478f3j 2 17 rational rational ADJ gb19f478f3j 2 18 curves curve NOUN gb19f478f3j 2 19 on on ADP gb19f478f3j 2 20 fano fano ADJ gb19f478f3j 2 21 varieties variety NOUN gb19f478f3j 2 22 . . PUNCT gb19f478f3j 3 1 for for ADP gb19f478f3j 3 2 a a DET gb19f478f3j 3 3 smooth smooth PROPN gb19f478f3j 3 4 fano fano PROPN gb19f478f3j 3 5 variety variety NOUN gb19f478f3j 3 6 x x PROPN gb19f478f3j 3 7 , , PUNCT gb19f478f3j 3 8 the the DET gb19f478f3j 3 9 conjecture conjecture NOUN gb19f478f3j 3 10 predicts predict VERB gb19f478f3j 3 11 there there PRON gb19f478f3j 3 12 is be VERB gb19f478f3j 3 13 a a DET gb19f478f3j 3 14 constant constant ADJ gb19f478f3j 3 15 bound bind VERB gb19f478f3j 3 16 on on ADP gb19f478f3j 3 17 the the DET gb19f478f3j 3 18 number number NOUN gb19f478f3j 3 19 of of ADP gb19f478f3j 3 20 manin manin ADJ gb19f478f3j 3 21 components component NOUN gb19f478f3j 3 22 of of ADP gb19f478f3j 3 23 the the DET gb19f478f3j 3 24 morphism morphism NOUN gb19f478f3j 3 25 scheme scheme NOUN gb19f478f3j 3 26 of of ADP gb19f478f3j 3 27 rational rational ADJ gb19f478f3j 3 28 curves curve NOUN gb19f478f3j 3 29 of of ADP gb19f478f3j 3 30 each each DET gb19f478f3j 3 31 numeric numeric ADJ gb19f478f3j 3 32 class class NOUN gb19f478f3j 3 33 . . PUNCT gb19f478f3j 4 1 on on ADP gb19f478f3j 4 2 a a DET gb19f478f3j 4 3 fano fano ADJ gb19f478f3j 4 4 threefold threefold NOUN gb19f478f3j 4 5 and and CCONJ gb19f478f3j 4 6 for for ADP gb19f478f3j 4 7 numeric numeric ADJ gb19f478f3j 4 8 classes class NOUN gb19f478f3j 4 9 of of ADP gb19f478f3j 4 10 anticanonical anticanonical ADJ gb19f478f3j 4 11 degree degree NOUN gb19f478f3j 4 12 at at ADV gb19f478f3j 4 13 least least ADJ gb19f478f3j 4 14 four four NUM gb19f478f3j 4 15 , , PUNCT gb19f478f3j 4 16 manin manin ADJ gb19f478f3j 4 17 components component NOUN gb19f478f3j 4 18 are be AUX gb19f478f3j 4 19 precisely precisely ADV gb19f478f3j 4 20 those those PRON gb19f478f3j 4 21 which which PRON gb19f478f3j 4 22 generically generically ADV gb19f478f3j 4 23 parameterize parameterize VERB gb19f478f3j 4 24 very very ADV gb19f478f3j 4 25 free free ADJ gb19f478f3j 4 26 curves curve NOUN gb19f478f3j 4 27 . . PUNCT gb19f478f3j 5 1 we we PRON gb19f478f3j 5 2 prove prove VERB gb19f478f3j 5 3 there there PRON gb19f478f3j 5 4 is be VERB gb19f478f3j 5 5 at at ADP gb19f478f3j 5 6 most most ADV gb19f478f3j 5 7 one one NUM gb19f478f3j 5 8 such such ADJ gb19f478f3j 5 9 component component NOUN gb19f478f3j 5 10 for for ADP gb19f478f3j 5 11 each each DET gb19f478f3j 5 12 numeric numeric ADJ gb19f478f3j 5 13 class class NOUN gb19f478f3j 5 14 . . PUNCT gb19f478f3j 6 1 first first ADV gb19f478f3j 6 2 , , PUNCT gb19f478f3j 6 3 we we PRON gb19f478f3j 6 4 describe describe VERB gb19f478f3j 6 5 how how SCONJ gb19f478f3j 6 6 a a DET gb19f478f3j 6 7 recent recent ADJ gb19f478f3j 6 8 , , PUNCT gb19f478f3j 6 9 movable movable ADJ gb19f478f3j 6 10 version version NOUN gb19f478f3j 6 11 of of ADP gb19f478f3j 6 12 mori mori PROPN gb19f478f3j 6 13 's 's PART gb19f478f3j 6 14 bend bend VERB gb19f478f3j 6 15 - - PUNCT gb19f478f3j 6 16 and and CCONJ gb19f478f3j 6 17 - - PUNCT gb19f478f3j 6 18 break break NOUN gb19f478f3j 6 19 for for ADP gb19f478f3j 6 20 free free ADJ gb19f478f3j 6 21 rational rational ADJ gb19f478f3j 6 22 curves curve NOUN gb19f478f3j 6 23 on on ADP gb19f478f3j 6 24 fano fano ADJ gb19f478f3j 6 25 threefolds threefold NOUN gb19f478f3j 6 26 reduces reduce VERB gb19f478f3j 6 27 geometric geometric ADJ gb19f478f3j 6 28 manin manin NOUN gb19f478f3j 6 29 's 's PART gb19f478f3j 6 30 conjecture conjecture NOUN gb19f478f3j 6 31 to to ADP gb19f478f3j 6 32 a a DET gb19f478f3j 6 33 study study NOUN gb19f478f3j 6 34 of of ADP gb19f478f3j 6 35 low low ADJ gb19f478f3j 6 36 degree degree NOUN gb19f478f3j 6 37 free free ADJ gb19f478f3j 6 38 curves curve NOUN gb19f478f3j 6 39 . . PUNCT gb19f478f3j 7 1 we we PRON gb19f478f3j 7 2 then then ADV gb19f478f3j 7 3 establish establish VERB gb19f478f3j 7 4 monodromy monodromy ADJ gb19f478f3j 7 5 properties property NOUN gb19f478f3j 7 6 of of ADP gb19f478f3j 7 7 mori mori NOUN gb19f478f3j 7 8 fiber fiber NOUN gb19f478f3j 7 9 space space NOUN gb19f478f3j 7 10 structures structure NOUN gb19f478f3j 7 11 on on ADP gb19f478f3j 7 12 fano fano ADJ gb19f478f3j 7 13 threefolds threefold NOUN gb19f478f3j 7 14 that that PRON gb19f478f3j 7 15 are be AUX gb19f478f3j 7 16 general general ADJ gb19f478f3j 7 17 in in ADP gb19f478f3j 7 18 their their PRON gb19f478f3j 7 19 deformation deformation NOUN gb19f478f3j 7 20 class class NOUN gb19f478f3j 7 21 . . PUNCT gb19f478f3j 8 1 this this PRON gb19f478f3j 8 2 allows allow VERB gb19f478f3j 8 3 us we PRON gb19f478f3j 8 4 to to PART gb19f478f3j 8 5 describe describe VERB gb19f478f3j 8 6 families family NOUN gb19f478f3j 8 7 of of ADP gb19f478f3j 8 8 low low ADJ gb19f478f3j 8 9 degree degree NOUN gb19f478f3j 8 10 free free ADJ gb19f478f3j 8 11 rational rational ADJ gb19f478f3j 8 12 curves curve NOUN gb19f478f3j 8 13 explicitly explicitly ADV gb19f478f3j 8 14 on on ADP gb19f478f3j 8 15 such such ADJ gb19f478f3j 8 16 threefolds threefold NOUN gb19f478f3j 8 17 . . PUNCT gb19f478f3j 9 1 where where SCONJ gb19f478f3j 9 2 necessary necessary ADJ gb19f478f3j 9 3 , , PUNCT gb19f478f3j 9 4 we we PRON gb19f478f3j 9 5 then then ADV gb19f478f3j 9 6 prove prove VERB gb19f478f3j 9 7 the the DET gb19f478f3j 9 8 number number NOUN gb19f478f3j 9 9 of of ADP gb19f478f3j 9 10 manin manin ADJ gb19f478f3j 9 11 components component NOUN gb19f478f3j 9 12 of of ADP gb19f478f3j 9 13 curves curve NOUN gb19f478f3j 9 14 remains remain VERB gb19f478f3j 9 15 constant constant ADJ gb19f478f3j 9 16 under under ADP gb19f478f3j 9 17 specialization specialization NOUN gb19f478f3j 9 18 of of ADP gb19f478f3j 9 19 x. x. PROPN gb19f478f3j 10 1 we we PRON gb19f478f3j 10 2 conclude conclude VERB gb19f478f3j 10 3 with with ADP gb19f478f3j 10 4 a a DET gb19f478f3j 10 5 case case NOUN gb19f478f3j 10 6 - - PUNCT gb19f478f3j 10 7 by by ADP gb19f478f3j 10 8 - - PUNCT gb19f478f3j 10 9 case case NOUN gb19f478f3j 10 10 analysis analysis NOUN gb19f478f3j 10 11 of of ADP gb19f478f3j 10 12 the the DET gb19f478f3j 10 13 88 88 NUM gb19f478f3j 10 14 deformation deformation NOUN gb19f478f3j 10 15 types type NOUN gb19f478f3j 10 16 of of ADP gb19f478f3j 10 17 smooth smooth ADJ gb19f478f3j 10 18 fano fano PROPN gb19f478f3j 10 19 threefolds threefold NOUN gb19f478f3j 10 20 of of ADP gb19f478f3j 10 21 picard picard NOUN gb19f478f3j 10 22 rank rank NOUN gb19f478f3j 10 23 at at ADV gb19f478f3j 10 24 least least ADJ gb19f478f3j 10 25 two two NUM gb19f478f3j 10 26 . . PUNCT