id	sid	tid	token	lemma	pos
g732d79512m	1	1	let	let	VERB
g732d79512m	1	2	g	g	NOUN
g732d79512m	1	3	be	be	AUX
g732d79512m	1	4	a	a	DET
g732d79512m	1	5	connected	connect	VERB
g732d79512m	1	6	linear	linear	ADJ
g732d79512m	1	7	algebraic	algebraic	ADJ
g732d79512m	1	8	group	group	NOUN
g732d79512m	1	9	acting	act	VERB
g732d79512m	1	10	on	on	ADP
g732d79512m	1	11	a	a	DET
g732d79512m	1	12	smooth	smooth	ADJ
g732d79512m	1	13	complex	complex	ADJ
g732d79512m	1	14	variety	variety	NOUN
g732d79512m	1	15	x	x	PUNCT
g732d79512m	1	16	with	with	ADP
g732d79512m	1	17	finitely	finitely	ADV
g732d79512m	1	18	many	many	ADJ
g732d79512m	1	19	orbits	orbit	NOUN
g732d79512m	1	20	.	.	PUNCT
g732d79512m	2	1	in	in	ADP
g732d79512m	2	2	this	this	DET
g732d79512m	2	3	case	case	NOUN
g732d79512m	2	4	,	,	PUNCT
g732d79512m	2	5	the	the	DET
g732d79512m	2	6	category	category	NOUN
g732d79512m	2	7	of	of	ADP
g732d79512m	2	8	g	g	NOUN
g732d79512m	2	9	-	-	PUNCT
g732d79512m	2	10	equivariant	equivariant	ADJ
g732d79512m	2	11	d	d	NOUN
g732d79512m	2	12	-	-	NOUN
g732d79512m	2	13	modules	module	NOUN
g732d79512m	2	14	is	be	AUX
g732d79512m	2	15	equivalent	equivalent	ADJ
g732d79512m	2	16	to	to	ADP
g732d79512m	2	17	the	the	DET
g732d79512m	2	18	category	category	NOUN
g732d79512m	2	19	of	of	ADP
g732d79512m	2	20	finite	finite	ADJ
g732d79512m	2	21	dimensional	dimensional	ADJ
g732d79512m	2	22	representations	representation	NOUN
g732d79512m	2	23	of	of	ADP
g732d79512m	2	24	a	a	DET
g732d79512m	2	25	quiver	quiver	NOUN
g732d79512m	2	26	with	with	ADP
g732d79512m	2	27	relations	relation	NOUN
g732d79512m	2	28	,	,	PUNCT
g732d79512m	2	29	and	and	CCONJ
g732d79512m	2	30	one	one	PRON
g732d79512m	2	31	may	may	AUX
g732d79512m	2	32	take	take	VERB
g732d79512m	2	33	advantage	advantage	NOUN
g732d79512m	2	34	of	of	ADP
g732d79512m	2	35	this	this	DET
g732d79512m	2	36	structure	structure	NOUN
g732d79512m	2	37	to	to	PART
g732d79512m	2	38	study	study	VERB
g732d79512m	2	39	the	the	DET
g732d79512m	2	40	local	local	ADJ
g732d79512m	2	41	cohomology	cohomology	NOUN
g732d79512m	2	42	modules	module	NOUN
g732d79512m	2	43	with	with	ADP
g732d79512m	2	44	support	support	NOUN
g732d79512m	2	45	in	in	ADP
g732d79512m	2	46	the	the	DET
g732d79512m	2	47	g	g	PROPN
g732d79512m	2	48	-	-	PUNCT
g732d79512m	2	49	stable	stable	ADJ
g732d79512m	2	50	subvarieties	subvarietie	NOUN
g732d79512m	2	51	of	of	ADP
g732d79512m	2	52	x.this	x.this	PRON
g732d79512m	2	53	thesis	thesis	NOUN
g732d79512m	2	54	is	be	AUX
g732d79512m	2	55	dedicated	dedicate	VERB
g732d79512m	2	56	to	to	ADP
g732d79512m	2	57	investigating	investigate	VERB
g732d79512m	2	58	categories	category	NOUN
g732d79512m	2	59	of	of	ADP
g732d79512m	2	60	g	g	NOUN
g732d79512m	2	61	-	-	PUNCT
g732d79512m	2	62	equivariant	equivariant	ADJ
g732d79512m	2	63	d	d	NOUN
g732d79512m	2	64	-	-	NOUN
g732d79512m	2	65	modules	module	NOUN
g732d79512m	2	66	and	and	CCONJ
g732d79512m	2	67	local	local	ADJ
g732d79512m	2	68	cohomology	cohomology	NOUN
g732d79512m	2	69	on	on	ADP
g732d79512m	2	70	vinberg	vinberg	NOUN
g732d79512m	2	71	representations	representation	NOUN
g732d79512m	2	72	,	,	PUNCT
g732d79512m	2	73	i.e.	i.e.	ADV
g732d79512m	2	74	when	when	SCONJ
g732d79512m	2	75	x	x	SYM
g732d79512m	2	76	is	be	AUX
g732d79512m	2	77	an	an	DET
g732d79512m	2	78	irreducible	irreducible	ADJ
g732d79512m	2	79	representation	representation	NOUN
g732d79512m	2	80	of	of	ADP
g732d79512m	2	81	g	g	PROPN
g732d79512m	2	82	,	,	PUNCT
g732d79512m	2	83	thought	think	VERB
g732d79512m	2	84	of	of	ADP
g732d79512m	2	85	as	as	ADP
g732d79512m	2	86	an	an	DET
g732d79512m	2	87	affine	affine	ADJ
g732d79512m	2	88	space	space	NOUN
g732d79512m	2	89	,	,	PUNCT
g732d79512m	2	90	and	and	CCONJ
g732d79512m	2	91	g	g	PROPN
g732d79512m	2	92	is	be	AUX
g732d79512m	2	93	reductive	reductive	ADJ
g732d79512m	2	94	.	.	PUNCT
g732d79512m	3	1	such	such	ADJ
g732d79512m	3	2	representations	representation	NOUN
g732d79512m	3	3	have	have	AUX
g732d79512m	3	4	been	be	AUX
g732d79512m	3	5	classified	classify	VERB
g732d79512m	3	6	,	,	PUNCT
g732d79512m	3	7	and	and	CCONJ
g732d79512m	3	8	correspond	correspond	VERB
g732d79512m	3	9	to	to	ADP
g732d79512m	3	10	a	a	DET
g732d79512m	3	11	choice	choice	NOUN
g732d79512m	3	12	of	of	ADP
g732d79512m	3	13	dynkin	dynkin	ADJ
g732d79512m	3	14	diagram	diagram	NOUN
g732d79512m	3	15	and	and	CCONJ
g732d79512m	3	16	vertex.when	vertex.when	NOUN
g732d79512m	3	17	x	x	PUNCT
g732d79512m	3	18	is	be	AUX
g732d79512m	3	19	the	the	DET
g732d79512m	3	20	space	space	NOUN
g732d79512m	3	21	of	of	ADP
g732d79512m	3	22	2x2x2	2x2x2	NUM
g732d79512m	3	23	hypermatrices	hypermatrice	NOUN
g732d79512m	3	24	endowed	endow	VERB
g732d79512m	3	25	with	with	ADP
g732d79512m	3	26	the	the	DET
g732d79512m	3	27	natural	natural	ADJ
g732d79512m	3	28	action	action	NOUN
g732d79512m	3	29	of	of	ADP
g732d79512m	3	30	g=	g=	PROPN
g732d79512m	3	31	gl_2	gl_2	PROPN
g732d79512m	3	32	x	x	PUNCT
g732d79512m	4	1	gl_2	gl_2	INTJ
g732d79512m	4	2	x	x	PUNCT
g732d79512m	4	3	gl_2	gl_2	INTJ
g732d79512m	4	4	,	,	PUNCT
g732d79512m	4	5	or	or	CCONJ
g732d79512m	4	6	when	when	SCONJ
g732d79512m	4	7	x	x	SYM
g732d79512m	4	8	is	be	AUX
g732d79512m	4	9	the	the	DET
g732d79512m	4	10	space	space	NOUN
g732d79512m	4	11	of	of	ADP
g732d79512m	4	12	alternating	alternate	VERB
g732d79512m	4	13	senary	senary	ADJ
g732d79512m	4	14	3	3	NUM
g732d79512m	4	15	-	-	PUNCT
g732d79512m	4	16	tensors	tensor	NOUN
g732d79512m	4	17	endowed	endow	VERB
g732d79512m	4	18	with	with	ADP
g732d79512m	4	19	the	the	DET
g732d79512m	4	20	natural	natural	ADJ
g732d79512m	4	21	action	action	NOUN
g732d79512m	4	22	of	of	ADP
g732d79512m	4	23	g	g	NOUN
g732d79512m	4	24	=	=	NOUN
g732d79512m	4	25	gl_6	gl_6	PROPN
g732d79512m	4	26	,	,	PUNCT
g732d79512m	4	27	our	our	PRON
g732d79512m	4	28	analysis	analysis	NOUN
g732d79512m	4	29	entails	entail	VERB
g732d79512m	4	30	:	:	PUNCT
g732d79512m	4	31	classifying	classify	VERB
g732d79512m	4	32	and	and	CCONJ
g732d79512m	4	33	explicitly	explicitly	ADV
g732d79512m	4	34	realizing	realize	VERB
g732d79512m	4	35	the	the	DET
g732d79512m	4	36	simple	simple	ADJ
g732d79512m	4	37	equivariant	equivariant	NOUN
g732d79512m	4	38	d	d	NOUN
g732d79512m	4	39	-	-	NOUN
g732d79512m	4	40	modules	module	NOUN
g732d79512m	4	41	,	,	PUNCT
g732d79512m	4	42	and	and	CCONJ
g732d79512m	4	43	determining	determine	VERB
g732d79512m	4	44	the	the	DET
g732d79512m	4	45	corresponding	corresponding	ADJ
g732d79512m	4	46	quiver	quiver	NOUN
g732d79512m	4	47	with	with	ADP
g732d79512m	4	48	relations	relation	NOUN
g732d79512m	4	49	.	.	PUNCT
g732d79512m	5	1	the	the	DET
g732d79512m	5	2	latter	latter	ADJ
g732d79512m	5	3	case	case	NOUN
g732d79512m	5	4	is	be	AUX
g732d79512m	5	5	joint	joint	ADJ
g732d79512m	5	6	work	work	NOUN
g732d79512m	5	7	with	with	ADP
g732d79512m	5	8	andrás	andrás	PROPN
g732d79512m	5	9	c.	c.	PROPN
g732d79512m	5	10	lőrincz	lőrincz	PROPN
g732d79512m	5	11	.	.	PUNCT
g732d79512m	6	1	as	as	ADP
g732d79512m	6	2	an	an	DET
g732d79512m	6	3	application	application	NOUN
g732d79512m	6	4	,	,	PUNCT
g732d79512m	6	5	we	we	PRON
g732d79512m	6	6	calculate	calculate	VERB
g732d79512m	6	7	local	local	ADJ
g732d79512m	6	8	cohomology	cohomology	NOUN
g732d79512m	6	9	with	with	ADP
g732d79512m	6	10	support	support	NOUN
g732d79512m	6	11	in	in	ADP
g732d79512m	6	12	the	the	DET
g732d79512m	6	13	orbit	orbit	NOUN
g732d79512m	6	14	closures	closure	NOUN
g732d79512m	6	15	,	,	PUNCT
g732d79512m	6	16	and	and	CCONJ
g732d79512m	6	17	obtain	obtain	VERB
g732d79512m	6	18	the	the	DET
g732d79512m	6	19	lyubeznik	lyubeznik	ADJ
g732d79512m	6	20	numbers.in	numbers.in	X
g732d79512m	6	21	another	another	DET
g732d79512m	6	22	direction	direction	NOUN
g732d79512m	6	23	,	,	PUNCT
g732d79512m	6	24	we	we	PRON
g732d79512m	6	25	determine	determine	VERB
g732d79512m	6	26	the	the	DET
g732d79512m	6	27	d	d	NOUN
g732d79512m	6	28	-	-	PUNCT
g732d79512m	6	29	module	module	NOUN
g732d79512m	6	30	structure	structure	NOUN
g732d79512m	6	31	of	of	ADP
g732d79512m	6	32	local	local	ADJ
g732d79512m	6	33	cohomology	cohomology	NOUN
g732d79512m	6	34	with	with	ADP
g732d79512m	6	35	support	support	NOUN
g732d79512m	6	36	in	in	ADP
g732d79512m	6	37	pfaffian	pfaffian	ADJ
g732d79512m	6	38	varieties	variety	NOUN
g732d79512m	6	39	,	,	PUNCT
g732d79512m	6	40	in	in	ADP
g732d79512m	6	41	which	which	DET
g732d79512m	6	42	case	case	NOUN
g732d79512m	6	43	the	the	DET
g732d79512m	6	44	simple	simple	ADJ
g732d79512m	6	45	composition	composition	NOUN
g732d79512m	6	46	factors	factor	NOUN
g732d79512m	6	47	were	be	AUX
g732d79512m	6	48	known	know	VERB
g732d79512m	6	49	by	by	ADP
g732d79512m	6	50	past	past	ADJ
g732d79512m	6	51	work	work	NOUN
g732d79512m	6	52	of	of	ADP
g732d79512m	6	53	raicu	raicu	NOUN
g732d79512m	6	54	-	-	PUNCT
g732d79512m	6	55	weyman	weyman	NOUN
g732d79512m	6	56	.	.	PUNCT
g732d79512m	7	1	this	this	DET
g732d79512m	7	2	information	information	NOUN
g732d79512m	7	3	,	,	PUNCT
g732d79512m	7	4	combined	combine	VERB
g732d79512m	7	5	with	with	ADP
g732d79512m	7	6	careful	careful	ADJ
g732d79512m	7	7	use	use	NOUN
g732d79512m	7	8	of	of	ADP
g732d79512m	7	9	graded	grade	VERB
g732d79512m	7	10	local	local	ADJ
g732d79512m	7	11	duality	duality	NOUN
g732d79512m	7	12	allows	allow	VERB
g732d79512m	7	13	us	we	PRON
g732d79512m	7	14	to	to	PART
g732d79512m	7	15	calculate	calculate	VERB
g732d79512m	7	16	the	the	DET
g732d79512m	7	17	lyubeznik	lyubeznik	ADJ
g732d79512m	7	18	numbers	number	NOUN
g732d79512m	7	19	for	for	ADP
g732d79512m	7	20	pfaffian	pfaffian	ADJ
g732d79512m	7	21	varieties	variety	NOUN
g732d79512m	7	22	.	.	PUNCT
g732d79512m	8	1	a	a	DET
g732d79512m	8	2	major	major	ADJ
g732d79512m	8	3	step	step	NOUN
g732d79512m	8	4	in	in	ADP
g732d79512m	8	5	this	this	DET
g732d79512m	8	6	work	work	NOUN
g732d79512m	8	7	is	be	AUX
g732d79512m	8	8	our	our	PRON
g732d79512m	8	9	computations	computation	NOUN
g732d79512m	8	10	of	of	ADP
g732d79512m	8	11	ext^j_s(s	ext^j_s(s	SPACE
g732d79512m	8	12	/	/	SYM
g732d79512m	8	13	i	i	PRON
g732d79512m	8	14	,	,	PUNCT
g732d79512m	8	15	s	s	NOUN
g732d79512m	8	16	)	)	PUNCT
g732d79512m	8	17	,	,	PUNCT
g732d79512m	8	18	where	where	SCONJ
g732d79512m	8	19	s	s	VERB
g732d79512m	8	20	is	be	AUX
g732d79512m	8	21	the	the	DET
g732d79512m	8	22	coordinate	coordinate	NOUN
g732d79512m	8	23	ring	ring	NOUN
g732d79512m	8	24	of	of	ADP
g732d79512m	8	25	the	the	DET
g732d79512m	8	26	space	space	NOUN
g732d79512m	8	27	of	of	ADP
g732d79512m	8	28	skew	skew	ADV
g732d79512m	8	29	-	-	PUNCT
g732d79512m	8	30	symmetric	symmetric	ADJ
g732d79512m	8	31	matrices	matrix	NOUN
g732d79512m	8	32	and	and	CCONJ
g732d79512m	8	33	i	i	PRON
g732d79512m	8	34	is	be	AUX
g732d79512m	8	35	a	a	DET
g732d79512m	8	36	g	g	ADJ
g732d79512m	8	37	-	-	PUNCT
g732d79512m	8	38	invariant	invariant	ADJ
g732d79512m	8	39	ideal	ideal	NOUN
g732d79512m	8	40	.	.	PUNCT
g732d79512m	9	1	as	as	ADP
g732d79512m	9	2	another	another	DET
g732d79512m	9	3	application	application	NOUN
g732d79512m	9	4	of	of	ADP
g732d79512m	9	5	these	these	DET
g732d79512m	9	6	ext	ext	ADJ
g732d79512m	9	7	results	result	NOUN
g732d79512m	9	8	,	,	PUNCT
g732d79512m	9	9	we	we	PRON
g732d79512m	9	10	determine	determine	VERB
g732d79512m	9	11	the	the	DET
g732d79512m	9	12	castelnuovo	castelnuovo	PROPN
g732d79512m	9	13	-	-	PUNCT
g732d79512m	9	14	mumford	mumford	ADJ
g732d79512m	9	15	regularity	regularity	NOUN
g732d79512m	9	16	of	of	ADP
g732d79512m	9	17	powers	power	NOUN
g732d79512m	9	18	and	and	CCONJ
g732d79512m	9	19	symbolic	symbolic	ADJ
g732d79512m	9	20	powers	power	NOUN
g732d79512m	9	21	of	of	ADP
g732d79512m	9	22	ideals	ideal	NOUN
g732d79512m	9	23	of	of	ADP
g732d79512m	9	24	pfaffians	pfaffian	NOUN
g732d79512m	9	25	.	.	PUNCT