id	sid	tid	token	lemma	pos
h702q527g73	1	1	an	an	DET
h702q527g73	1	2	ideal	ideal	ADJ
h702q527g73	1	3	j	j	NOUN
h702q527g73	1	4	is	be	AUX
h702q527g73	1	5	said	say	VERB
h702q527g73	1	6	to	to	PART
h702q527g73	1	7	be	be	AUX
h702q527g73	1	8	numerically	numerically	ADV
h702q527g73	1	9	c	c	NOUN
h702q527g73	1	10	-	-	PUNCT
h702q527g73	1	11	acm	acm	PROPN
h702q527g73	1	12	(	(	PUNCT
h702q527g73	1	13	nacm	nacm	PROPN
h702q527g73	1	14	)	)	PUNCT
h702q527g73	1	15	if	if	SCONJ
h702q527g73	1	16	r	r	NOUN
h702q527g73	1	17	/	/	SYM
h702q527g73	1	18	j	j	PROPN
h702q527g73	1	19	has	have	VERB
h702q527g73	1	20	the	the	DET
h702q527g73	1	21	hilbert	hilbert	PROPN
h702q527g73	1	22	function	function	NOUN
h702q527g73	1	23	of	of	ADP
h702q527g73	1	24	some	some	DET
h702q527g73	1	25	codimension	codimension	NOUN
h702q527g73	1	26	c	c	NOUN
h702q527g73	1	27	acm	acm	NOUN
h702q527g73	1	28	subscheme	subscheme	NOUN
h702q527g73	1	29	of	of	ADP
h702q527g73	1	30	p^n	p^n	PROPN
h702q527g73	1	31	.	.	PUNCT
h702q527g73	2	1	we	we	PRON
h702q527g73	2	2	exhibit	exhibit	VERB
h702q527g73	2	3	algorithm	algorithm	NOUN
h702q527g73	2	4	which	which	PRON
h702q527g73	2	5	takes	take	VERB
h702q527g73	2	6	an	an	DET
h702q527g73	2	7	arbitrary	arbitrary	ADJ
h702q527g73	2	8	ideal	ideal	NOUN
h702q527g73	2	9	and	and	CCONJ
h702q527g73	2	10	produces	produce	VERB
h702q527g73	2	11	,	,	PUNCT
h702q527g73	2	12	via	via	ADP
h702q527g73	2	13	a	a	DET
h702q527g73	2	14	finite	finite	ADJ
h702q527g73	2	15	sequence	sequence	NOUN
h702q527g73	2	16	of	of	ADP
h702q527g73	2	17	basic	basic	ADJ
h702q527g73	2	18	double	double	ADJ
h702q527g73	2	19	links	link	NOUN
h702q527g73	2	20	,	,	PUNCT
h702q527g73	2	21	an	an	DET
h702q527g73	2	22	ideal	ideal	NOUN
h702q527g73	2	23	which	which	PRON
h702q527g73	2	24	is	be	AUX
h702q527g73	2	25	numerically	numerically	ADV
h702q527g73	2	26	c	c	NOUN
h702q527g73	2	27	-	-	PUNCT
h702q527g73	2	28	acm	acm	NOUN
h702q527g73	2	29	.	.	PUNCT
h702q527g73	3	1	an	an	DET
h702q527g73	3	2	immediate	immediate	ADJ
h702q527g73	3	3	consequence	consequence	NOUN
h702q527g73	3	4	of	of	ADP
h702q527g73	3	5	this	this	DET
h702q527g73	3	6	result	result	NOUN
h702q527g73	3	7	is	be	AUX
h702q527g73	3	8	that	that	SCONJ
h702q527g73	3	9	every	every	DET
h702q527g73	3	10	even	even	ADJ
h702q527g73	3	11	liaison	liaison	NOUN
h702q527g73	3	12	class	class	NOUN
h702q527g73	3	13	of	of	ADP
h702q527g73	3	14	equidimensional	equidimensional	ADJ
h702q527g73	3	15	codimension	codimension	NOUN
h702q527g73	3	16	c	c	NOUN
h702q527g73	3	17	subschemes	subscheme	NOUN
h702q527g73	3	18	of	of	ADP
h702q527g73	3	19	p^n	p^n	PROPN
h702q527g73	3	20	contains	contain	VERB
h702q527g73	3	21	elements	element	NOUN
h702q527g73	3	22	which	which	PRON
h702q527g73	3	23	are	be	AUX
h702q527g73	3	24	nacm	nacm	ADJ
h702q527g73	3	25	.	.	PUNCT
h702q527g73	4	1	this	this	PRON
h702q527g73	4	2	was	be	AUX
h702q527g73	4	3	first	first	ADV
h702q527g73	4	4	proved	prove	VERB
h702q527g73	4	5	for	for	ADP
h702q527g73	4	6	the	the	DET
h702q527g73	4	7	codimension	codimension	NOUN
h702q527g73	4	8	two	two	NUM
h702q527g73	4	9	case	case	NOUN
h702q527g73	4	10	by	by	ADP
h702q527g73	4	11	migliore	migliore	PROPN
h702q527g73	4	12	and	and	CCONJ
h702q527g73	4	13	nagel	nagel	PROPN
h702q527g73	4	14	,	,	PUNCT
h702q527g73	4	15	but	but	CCONJ
h702q527g73	4	16	was	be	AUX
h702q527g73	4	17	an	an	DET
h702q527g73	4	18	open	open	ADJ
h702q527g73	4	19	question	question	NOUN
h702q527g73	4	20	in	in	ADP
h702q527g73	4	21	higher	high	ADJ
h702q527g73	4	22	codimension	codimension	NOUN
h702q527g73	4	23	.	.	PUNCT
h702q527g73	5	1	let	let	VERB
h702q527g73	5	2	l	l	PRON
h702q527g73	5	3	denote	denote	VERB
h702q527g73	5	4	the	the	DET
h702q527g73	5	5	even	even	ADJ
h702q527g73	5	6	liaison	liaison	NOUN
h702q527g73	5	7	class	class	NOUN
h702q527g73	5	8	of	of	ADP
h702q527g73	5	9	three	three	NUM
h702q527g73	5	10	skew	skew	ADJ
h702q527g73	5	11	lines	line	NOUN
h702q527g73	5	12	in	in	ADP
h702q527g73	5	13	p^4	p^4	SPACE
h702q527g73	5	14	,	,	PUNCT
h702q527g73	5	15	and	and	CCONJ
h702q527g73	5	16	let	let	VERB
h702q527g73	5	17	l_s	l_s	SPACE
h702q527g73	5	18	be	be	AUX
h702q527g73	5	19	denote	denote	ADJ
h702q527g73	5	20	the	the	DET
h702q527g73	5	21	even	even	ADJ
h702q527g73	5	22	liaison	liaison	NOUN
h702q527g73	5	23	class	class	NOUN
h702q527g73	5	24	of	of	ADP
h702q527g73	5	25	three	three	NUM
h702q527g73	5	26	skew	skew	ADJ
h702q527g73	5	27	lines	line	NOUN
h702q527g73	5	28	on	on	ADP
h702q527g73	5	29	a	a	DET
h702q527g73	5	30	smooth	smooth	ADJ
h702q527g73	5	31	hypersurface	hypersurface	NOUN
h702q527g73	5	32	s	s	VERB
h702q527g73	5	33	in	in	ADP
h702q527g73	5	34	p^4	p^4	PRON
h702q527g73	5	35	of	of	ADP
h702q527g73	5	36	degree	degree	NOUN
h702q527g73	5	37	at	at	ADV
h702q527g73	5	38	least	least	ADJ
h702q527g73	5	39	two	two	NUM
h702q527g73	5	40	.	.	PUNCT
h702q527g73	6	1	we	we	PRON
h702q527g73	6	2	also	also	ADV
h702q527g73	6	3	give	give	VERB
h702q527g73	6	4	a	a	DET
h702q527g73	6	5	complete	complete	ADJ
h702q527g73	6	6	description	description	NOUN
h702q527g73	6	7	of	of	ADP
h702q527g73	6	8	the	the	DET
h702q527g73	6	9	sequences	sequence	NOUN
h702q527g73	6	10	of	of	ADP
h702q527g73	6	11	basic	basic	ADJ
h702q527g73	6	12	double	double	ADJ
h702q527g73	6	13	links	link	NOUN
h702q527g73	6	14	which	which	PRON
h702q527g73	6	15	(	(	PUNCT
h702q527g73	6	16	in	in	ADP
h702q527g73	6	17	s	s	PRON
h702q527g73	6	18	)	)	PUNCT
h702q527g73	6	19	produce	produce	VERB
h702q527g73	6	20	curves	curve	NOUN
h702q527g73	6	21	which	which	PRON
h702q527g73	6	22	are	be	AUX
h702q527g73	6	23	nacm	nacm	ADJ
h702q527g73	6	24	.	.	PUNCT
h702q527g73	7	1	we	we	PRON
h702q527g73	7	2	conclude	conclude	VERB
h702q527g73	7	3	by	by	ADP
h702q527g73	7	4	showing	show	VERB
h702q527g73	7	5	that	that	SCONJ
h702q527g73	7	6	the	the	DET
h702q527g73	7	7	subset	subset	NOUN
h702q527g73	7	8	of	of	ADP
h702q527g73	7	9	l_s	l_s	SPACE
h702q527g73	7	10	consisting	consist	VERB
h702q527g73	7	11	of	of	ADP
h702q527g73	7	12	nacm	nacm	ADJ
h702q527g73	7	13	subschemes	subscheme	NOUN
h702q527g73	7	14	,	,	PUNCT
h702q527g73	7	15	which	which	PRON
h702q527g73	7	16	we	we	PRON
h702q527g73	7	17	denote	denote	VERB
h702q527g73	7	18	by	by	ADP
h702q527g73	7	19	m_s	m_s	SPACE
h702q527g73	7	20	,	,	PUNCT
h702q527g73	7	21	fails	fail	VERB
h702q527g73	7	22	to	to	PART
h702q527g73	7	23	have	have	VERB
h702q527g73	7	24	the	the	DET
h702q527g73	7	25	lazarsfeld	lazarsfeld	PROPN
h702q527g73	7	26	-	-	PUNCT
h702q527g73	7	27	rao	rao	PROPN
h702q527g73	7	28	property	property	NOUN
h702q527g73	7	29	.	.	PUNCT