id	sid	tid	token	lemma	pos
6h440r9919t	1	1	the	the	DET
6h440r9919t	1	2	goal	goal	NOUN
6h440r9919t	1	3	of	of	ADP
6h440r9919t	1	4	this	this	DET
6h440r9919t	1	5	thesis	thesis	NOUN
6h440r9919t	1	6	is	be	AUX
6h440r9919t	1	7	to	to	PART
6h440r9919t	1	8	study	study	VERB
6h440r9919t	1	9	rees	ree	NOUN
6h440r9919t	1	10	algebra	algebra	NOUN
6h440r9919t	1	11	r(i	r(i	SPACE
6h440r9919t	1	12	)	)	PUNCT
6h440r9919t	1	13	and	and	CCONJ
6h440r9919t	1	14	the	the	DET
6h440r9919t	1	15	special	special	ADJ
6h440r9919t	1	16	fiber	fiber	NOUN
6h440r9919t	1	17	ring	ring	PROPN
6h440r9919t	1	18	f(i	f(i	PROPN
6h440r9919t	1	19	)	)	PUNCT
6h440r9919t	1	20	for	for	ADP
6h440r9919t	1	21	a	a	DET
6h440r9919t	1	22	family	family	NOUN
6h440r9919t	1	23	of	of	ADP
6h440r9919t	1	24	ideals	ideal	NOUN
6h440r9919t	1	25	.	.	PUNCT
6h440r9919t	2	1	given	give	VERB
6h440r9919t	2	2	a	a	DET
6h440r9919t	2	3	map	map	NOUN
6h440r9919t	2	4	between	between	ADP
6h440r9919t	2	5	projective	projective	ADJ
6h440r9919t	2	6	spaces	space	NOUN
6h440r9919t	2	7	parameterizing	parameterize	VERB
6h440r9919t	2	8	a	a	DET
6h440r9919t	2	9	variety	variety	NOUN
6h440r9919t	2	10	,	,	PUNCT
6h440r9919t	2	11	the	the	DET
6h440r9919t	2	12	rees	ree	NOUN
6h440r9919t	2	13	algebra	algebra	NOUN
6h440r9919t	2	14	is	be	AUX
6h440r9919t	2	15	the	the	DET
6h440r9919t	2	16	coordinate	coordinate	NOUN
6h440r9919t	2	17	ring	ring	NOUN
6h440r9919t	2	18	of	of	ADP
6h440r9919t	2	19	the	the	DET
6h440r9919t	2	20	graph	graph	NOUN
6h440r9919t	2	21	and	and	CCONJ
6h440r9919t	2	22	the	the	DET
6h440r9919t	2	23	special	special	ADJ
6h440r9919t	2	24	fiber	fiber	NOUN
6h440r9919t	2	25	ring	ring	NOUN
6h440r9919t	2	26	is	be	AUX
6h440r9919t	2	27	the	the	DET
6h440r9919t	2	28	coordinate	coordinate	NOUN
6h440r9919t	2	29	ring	ring	NOUN
6h440r9919t	2	30	of	of	ADP
6h440r9919t	2	31	the	the	DET
6h440r9919t	2	32	image	image	NOUN
6h440r9919t	2	33	.	.	PUNCT
6h440r9919t	3	1	we	we	PRON
6h440r9919t	3	2	will	will	AUX
6h440r9919t	3	3	compute	compute	VERB
6h440r9919t	3	4	the	the	DET
6h440r9919t	3	5	defining	define	VERB
6h440r9919t	3	6	ideal	ideal	NOUN
6h440r9919t	3	7	of	of	ADP
6h440r9919t	3	8	these	these	DET
6h440r9919t	3	9	algebras	algebra	NOUN
6h440r9919t	3	10	.	.	PUNCT
6h440r9919t	4	1	let	let	VERB
6h440r9919t	4	2	r	r	PROPN
6h440r9919t	4	3	=	=	PROPN
6h440r9919t	4	4	k[x_1	k[x_1	PROPN
6h440r9919t	4	5	,	,	PUNCT
6h440r9919t	4	6	...	...	PUNCT
6h440r9919t	4	7	,	,	PUNCT
6h440r9919t	4	8	x_d	x_d	PUNCT
6h440r9919t	4	9	]	]	PUNCT
6h440r9919t	4	10	for	for	ADP
6h440r9919t	4	11	d	d	NOUN
6h440r9919t	4	12	greater	great	ADJ
6h440r9919t	4	13	than	than	ADP
6h440r9919t	4	14	or	or	CCONJ
6h440r9919t	4	15	equal	equal	ADJ
6h440r9919t	4	16	to	to	ADP
6h440r9919t	4	17	4	4	NUM
6h440r9919t	4	18	be	be	AUX
6h440r9919t	4	19	a	a	DET
6h440r9919t	4	20	polynomial	polynomial	ADJ
6h440r9919t	4	21	ring	ring	NOUN
6h440r9919t	4	22	with	with	ADP
6h440r9919t	4	23	homogeneous	homogeneous	ADJ
6h440r9919t	4	24	maximal	maximal	ADJ
6h440r9919t	4	25	ideal	ideal	ADJ
6h440r9919t	4	26	m.	m.	NOUN
6h440r9919t	4	27	we	we	PRON
6h440r9919t	4	28	study	study	VERB
6h440r9919t	4	29	the	the	DET
6h440r9919t	4	30	r	r	NOUN
6h440r9919t	4	31	-	-	PUNCT
6h440r9919t	4	32	ideals	ideal	NOUN
6h440r9919t	4	33	i	i	PRON
6h440r9919t	4	34	which	which	PRON
6h440r9919t	4	35	are	be	AUX
6h440r9919t	4	36	m	m	NOUN
6h440r9919t	4	37	-	-	ADJ
6h440r9919t	4	38	primary	primary	ADJ
6h440r9919t	4	39	,	,	PUNCT
6h440r9919t	4	40	gorenstein	gorenstein	NOUN
6h440r9919t	4	41	,	,	PUNCT
6h440r9919t	4	42	generated	generate	VERB
6h440r9919t	4	43	in	in	ADP
6h440r9919t	4	44	degree	degree	NOUN
6h440r9919t	4	45	2	2	NUM
6h440r9919t	4	46	,	,	PUNCT
6h440r9919t	4	47	and	and	CCONJ
6h440r9919t	4	48	have	have	VERB
6h440r9919t	4	49	a	a	DET
6h440r9919t	4	50	gorenstein	gorenstein	ADJ
6h440r9919t	4	51	linear	linear	ADJ
6h440r9919t	4	52	resolution	resolution	NOUN
6h440r9919t	4	53	.	.	PUNCT
6h440r9919t	5	1	the	the	DET
6h440r9919t	5	2	defining	define	VERB
6h440r9919t	5	3	ideal	ideal	NOUN
6h440r9919t	5	4	of	of	ADP
6h440r9919t	5	5	the	the	DET
6h440r9919t	5	6	rees	ree	NOUN
6h440r9919t	5	7	algebra	algebra	NOUN
6h440r9919t	5	8	will	will	AUX
6h440r9919t	5	9	be	be	AUX
6h440r9919t	5	10	of	of	ADP
6h440r9919t	5	11	fiber	fiber	NOUN
6h440r9919t	5	12	type	type	NOUN
6h440r9919t	5	13	.	.	PUNCT
6h440r9919t	6	1	that	that	ADV
6h440r9919t	6	2	is	is	ADV
6h440r9919t	6	3	,	,	PUNCT
6h440r9919t	6	4	the	the	DET
6h440r9919t	6	5	defining	define	VERB
6h440r9919t	6	6	ideal	ideal	NOUN
6h440r9919t	6	7	of	of	ADP
6h440r9919t	6	8	the	the	DET
6h440r9919t	6	9	rees	ree	NOUN
6h440r9919t	6	10	algebra	algebra	NOUN
6h440r9919t	6	11	is	be	AUX
6h440r9919t	6	12	generated	generate	VERB
6h440r9919t	6	13	by	by	ADP
6h440r9919t	6	14	the	the	DET
6h440r9919t	6	15	defining	define	VERB
6h440r9919t	6	16	ideals	ideal	NOUN
6h440r9919t	6	17	of	of	ADP
6h440r9919t	6	18	the	the	DET
6h440r9919t	6	19	special	special	ADJ
6h440r9919t	6	20	fiber	fiber	NOUN
6h440r9919t	6	21	ring	ring	NOUN
6h440r9919t	6	22	and	and	CCONJ
6h440r9919t	6	23	of	of	ADP
6h440r9919t	6	24	the	the	DET
6h440r9919t	6	25	symmetric	symmetric	ADJ
6h440r9919t	6	26	algebra	algebra	NOUN
6h440r9919t	6	27	.	.	PUNCT
6h440r9919t	7	1	the	the	DET
6h440r9919t	7	2	defining	define	VERB
6h440r9919t	7	3	ideal	ideal	NOUN
6h440r9919t	7	4	of	of	ADP
6h440r9919t	7	5	the	the	DET
6h440r9919t	7	6	symmetric	symmetric	ADJ
6h440r9919t	7	7	algebra	algebra	NOUN
6h440r9919t	7	8	is	be	AUX
6h440r9919t	7	9	well	well	ADV
6h440r9919t	7	10	understood	understand	VERB
6h440r9919t	7	11	,	,	PUNCT
6h440r9919t	7	12	so	so	ADV
6h440r9919t	7	13	we	we	PRON
6h440r9919t	7	14	concentrate	concentrate	VERB
6h440r9919t	7	15	on	on	ADP
6h440r9919t	7	16	computing	compute	VERB
6h440r9919t	7	17	the	the	DET
6h440r9919t	7	18	defining	define	VERB
6h440r9919t	7	19	ideal	ideal	NOUN
6h440r9919t	7	20	of	of	ADP
6h440r9919t	7	21	the	the	DET
6h440r9919t	7	22	special	special	ADJ
6h440r9919t	7	23	fiber	fiber	NOUN
6h440r9919t	7	24	ring	ring	NOUN
6h440r9919t	7	25	.	.	PUNCT
6h440r9919t	8	1	in	in	ADP
6h440r9919t	8	2	chapter	chapter	NOUN
6h440r9919t	8	3	4	4	NUM
6h440r9919t	8	4	,	,	PUNCT
6h440r9919t	8	5	the	the	DET
6h440r9919t	8	6	defining	define	VERB
6h440r9919t	8	7	ideal	ideal	NOUN
6h440r9919t	8	8	of	of	ADP
6h440r9919t	8	9	the	the	DET
6h440r9919t	8	10	special	special	ADJ
6h440r9919t	8	11	fiber	fiber	NOUN
6h440r9919t	8	12	ring	ring	PROPN
6h440r9919t	8	13	f(i	f(i	PROPN
6h440r9919t	8	14	)	)	PUNCT
6h440r9919t	8	15	will	will	AUX
6h440r9919t	8	16	be	be	AUX
6h440r9919t	8	17	given	give	VERB
6h440r9919t	8	18	as	as	ADP
6h440r9919t	8	19	a	a	DET
6h440r9919t	8	20	sub	sub	NOUN
6h440r9919t	8	21	-	-	NOUN
6h440r9919t	8	22	ideal	ideal	ADJ
6h440r9919t	8	23	of	of	ADP
6h440r9919t	8	24	the	the	DET
6h440r9919t	8	25	2x2	2x2	NUM
6h440r9919t	8	26	minors	minor	NOUN
6h440r9919t	8	27	of	of	ADP
6h440r9919t	8	28	a	a	DET
6h440r9919t	8	29	symmetric	symmetric	ADJ
6h440r9919t	8	30	matrix	matrix	NOUN
6h440r9919t	8	31	of	of	ADP
6h440r9919t	8	32	variables	variable	NOUN
6h440r9919t	8	33	modeled	model	VERB
6h440r9919t	8	34	after	after	ADP
6h440r9919t	8	35	the	the	DET
6h440r9919t	8	36	defining	define	VERB
6h440r9919t	8	37	ideal	ideal	NOUN
6h440r9919t	8	38	of	of	ADP
6h440r9919t	8	39	f(m^2	f(m^2	PROPN
6h440r9919t	8	40	)	)	PUNCT
6h440r9919t	8	41	.	.	PUNCT
6h440r9919t	9	1	in	in	ADP
6h440r9919t	9	2	chapter	chapter	NOUN
6h440r9919t	9	3	5	5	NUM
6h440r9919t	9	4	,	,	PUNCT
6h440r9919t	9	5	the	the	DET
6h440r9919t	9	6	defining	define	VERB
6h440r9919t	9	7	ideal	ideal	NOUN
6h440r9919t	9	8	of	of	ADP
6h440r9919t	9	9	the	the	DET
6h440r9919t	9	10	special	special	ADJ
6h440r9919t	9	11	fiber	fiber	NOUN
6h440r9919t	9	12	ring	ring	NOUN
6h440r9919t	9	13	of	of	ADP
6h440r9919t	9	14	i	i	PRON
6h440r9919t	9	15	will	will	AUX
6h440r9919t	9	16	be	be	AUX
6h440r9919t	9	17	described	describe	VERB
6h440r9919t	9	18	as	as	ADP
6h440r9919t	9	19	a	a	DET
6h440r9919t	9	20	saturation	saturation	NOUN
6h440r9919t	9	21	of	of	ADP
6h440r9919t	9	22	the	the	DET
6h440r9919t	9	23	maximal	maximal	ADJ
6h440r9919t	9	24	minors	minor	NOUN
6h440r9919t	9	25	of	of	ADP
6h440r9919t	9	26	the	the	DET
6h440r9919t	9	27	jacobian	jacobian	ADJ
6h440r9919t	9	28	dual	dual	NOUN
6h440r9919t	9	29	.	.	PUNCT
6h440r9919t	10	1	we	we	PRON
6h440r9919t	10	2	include	include	VERB
6h440r9919t	10	3	both	both	DET
6h440r9919t	10	4	descriptions	description	NOUN
6h440r9919t	10	5	of	of	ADP
6h440r9919t	10	6	the	the	DET
6h440r9919t	10	7	defining	define	VERB
6h440r9919t	10	8	ideal	ideal	NOUN
6h440r9919t	10	9	in	in	ADP
6h440r9919t	10	10	this	this	DET
6h440r9919t	10	11	manuscript	manuscript	NOUN
6h440r9919t	10	12	because	because	SCONJ
6h440r9919t	10	13	while	while	SCONJ
6h440r9919t	10	14	the	the	DET
6h440r9919t	10	15	methods	method	NOUN
6h440r9919t	10	16	in	in	ADP
6h440r9919t	10	17	chapter	chapter	NOUN
6h440r9919t	10	18	4	4	NUM
6h440r9919t	10	19	give	give	VERB
6h440r9919t	10	20	explicit	explicit	ADJ
6h440r9919t	10	21	polynomial	polynomial	ADJ
6h440r9919t	10	22	generators	generator	NOUN
6h440r9919t	10	23	of	of	ADP
6h440r9919t	10	24	the	the	DET
6h440r9919t	10	25	defining	define	VERB
6h440r9919t	10	26	ideal	ideal	NOUN
6h440r9919t	10	27	,	,	PUNCT
6h440r9919t	10	28	the	the	DET
6h440r9919t	10	29	methods	method	NOUN
6h440r9919t	10	30	in	in	ADP
6h440r9919t	10	31	chapter	chapter	NOUN
6h440r9919t	10	32	5	5	NUM
6h440r9919t	10	33	are	be	AUX
6h440r9919t	10	34	more	more	ADV
6h440r9919t	10	35	likely	likely	ADJ
6h440r9919t	10	36	to	to	PART
6h440r9919t	10	37	generalize	generalize	VERB
6h440r9919t	10	38	to	to	ADP
6h440r9919t	10	39	the	the	DET
6h440r9919t	10	40	larger	large	ADJ
6h440r9919t	10	41	class	class	NOUN
6h440r9919t	10	42	of	of	ADP
6h440r9919t	10	43	m	m	NOUN
6h440r9919t	10	44	-	-	ADJ
6h440r9919t	10	45	primary	primary	ADJ
6h440r9919t	10	46	gorenstein	gorenstein	NOUN
6h440r9919t	10	47	ideals	ideal	NOUN
6h440r9919t	10	48	having	have	VERB
6h440r9919t	10	49	a	a	DET
6h440r9919t	10	50	gorenstein	gorenstein	ADJ
6h440r9919t	10	51	linear	linear	ADJ
6h440r9919t	10	52	resolution	resolution	NOUN
6h440r9919t	10	53	.	.	PUNCT