id	sid	tid	token	lemma	pos
bv73bz62h3d	1	1	given	give	VERB
bv73bz62h3d	1	2	an	an	DET
bv73bz62h3d	1	3	ideal	ideal	NOUN
bv73bz62h3d	1	4	$	$	SYM
bv73bz62h3d	1	5	i$	i$	NOUN
bv73bz62h3d	1	6	in	in	ADP
bv73bz62h3d	1	7	a	a	DET
bv73bz62h3d	1	8	noetherian	noetherian	ADJ
bv73bz62h3d	1	9	ring	ring	NOUN
bv73bz62h3d	1	10	$	$	SYM
bv73bz62h3d	1	11	r$	r$	NOUN
bv73bz62h3d	1	12	,	,	PUNCT
bv73bz62h3d	1	13	the	the	DET
bv73bz62h3d	1	14	core	core	NOUN
bv73bz62h3d	1	15	of	of	ADP
bv73bz62h3d	1	16	$	$	SYM
bv73bz62h3d	1	17	i$	i$	NOUN
bv73bz62h3d	1	18	is	be	AUX
bv73bz62h3d	1	19	the	the	DET
bv73bz62h3d	1	20	intersection	intersection	NOUN
bv73bz62h3d	1	21	of	of	ADP
bv73bz62h3d	1	22	all	all	DET
bv73bz62h3d	1	23	ideals	ideal	NOUN
bv73bz62h3d	1	24	contained	contain	VERB
bv73bz62h3d	1	25	in	in	ADP
bv73bz62h3d	1	26	$	$	SYM
bv73bz62h3d	1	27	i$	i$	NOUN
bv73bz62h3d	1	28	with	with	ADP
bv73bz62h3d	1	29	the	the	DET
bv73bz62h3d	1	30	same	same	ADJ
bv73bz62h3d	1	31	integral	integral	ADJ
bv73bz62h3d	1	32	closure	closure	NOUN
bv73bz62h3d	1	33	as	as	ADP
bv73bz62h3d	1	34	$	$	SYM
bv73bz62h3d	1	35	i$.	i$.	VERB
bv73bz62h3d	1	36	the	the	DET
bv73bz62h3d	1	37	core	core	NOUN
bv73bz62h3d	1	38	naturally	naturally	ADV
bv73bz62h3d	1	39	arises	arise	VERB
bv73bz62h3d	1	40	in	in	ADP
bv73bz62h3d	1	41	the	the	DET
bv73bz62h3d	1	42	context	context	NOUN
bv73bz62h3d	1	43	of	of	ADP
bv73bz62h3d	1	44	the	the	DET
bv73bz62h3d	1	45	brianc{c}on	brianc{c}on	PROPN
bv73bz62h3d	1	46	-	-	PUNCT
bv73bz62h3d	1	47	skoda	skoda	NOUN
bv73bz62h3d	1	48	theorem	theorem	NOUN
bv73bz62h3d	1	49	as	as	ADP
bv73bz62h3d	1	50	an	an	DET
bv73bz62h3d	1	51	ideal	ideal	NOUN
bv73bz62h3d	1	52	which	which	PRON
bv73bz62h3d	1	53	contains	contain	VERB
bv73bz62h3d	1	54	the	the	DET
bv73bz62h3d	1	55	adjoint	adjoint	NOUN
bv73bz62h3d	1	56	of	of	ADP
bv73bz62h3d	1	57	a	a	DET
bv73bz62h3d	1	58	certain	certain	ADJ
bv73bz62h3d	1	59	power	power	NOUN
bv73bz62h3d	1	60	of	of	ADP
bv73bz62h3d	1	61	$	$	SYM
bv73bz62h3d	1	62	i$.	i$.	NOUN
bv73bz62h3d	1	63	as	as	ADP
bv73bz62h3d	1	64	the	the	DET
bv73bz62h3d	1	65	arbitrary	arbitrary	ADJ
bv73bz62h3d	1	66	-	-	PUNCT
bv73bz62h3d	1	67	characteristic	characteristic	ADJ
bv73bz62h3d	1	68	analog	analog	NOUN
bv73bz62h3d	1	69	of	of	ADP
bv73bz62h3d	1	70	the	the	DET
bv73bz62h3d	1	71	multiplier	multipli	ADJ
bv73bz62h3d	1	72	ideal	ideal	NOUN
bv73bz62h3d	1	73	,	,	PUNCT
bv73bz62h3d	1	74	the	the	DET
bv73bz62h3d	1	75	adjoint	adjoint	NOUN
bv73bz62h3d	1	76	is	be	AUX
bv73bz62h3d	1	77	an	an	DET
bv73bz62h3d	1	78	important	important	ADJ
bv73bz62h3d	1	79	tool	tool	NOUN
bv73bz62h3d	1	80	in	in	ADP
bv73bz62h3d	1	81	the	the	DET
bv73bz62h3d	1	82	study	study	NOUN
bv73bz62h3d	1	83	of	of	ADP
bv73bz62h3d	1	84	resolutions	resolution	NOUN
bv73bz62h3d	1	85	of	of	ADP
bv73bz62h3d	1	86	singularities	singularity	NOUN
bv73bz62h3d	1	87	.	.	PUNCT
bv73bz62h3d	2	1	the	the	DET
bv73bz62h3d	2	2	question	question	NOUN
bv73bz62h3d	2	3	of	of	ADP
bv73bz62h3d	2	4	when	when	SCONJ
bv73bz62h3d	2	5	the	the	DET
bv73bz62h3d	2	6	core	core	NOUN
bv73bz62h3d	2	7	and	and	CCONJ
bv73bz62h3d	2	8	the	the	DET
bv73bz62h3d	2	9	adjoint	adjoint	NOUN
bv73bz62h3d	2	10	of	of	ADP
bv73bz62h3d	2	11	a	a	DET
bv73bz62h3d	2	12	power	power	NOUN
bv73bz62h3d	2	13	of	of	ADP
bv73bz62h3d	2	14	$	$	SYM
bv73bz62h3d	2	15	i$	i$	NOUN
bv73bz62h3d	2	16	are	be	AUX
bv73bz62h3d	2	17	equal	equal	ADJ
bv73bz62h3d	2	18	has	have	AUX
bv73bz62h3d	2	19	been	be	AUX
bv73bz62h3d	2	20	tied	tie	VERB
bv73bz62h3d	2	21	to	to	ADP
bv73bz62h3d	2	22	a	a	DET
bv73bz62h3d	2	23	celebrated	celebrated	ADJ
bv73bz62h3d	2	24	conjecture	conjecture	NOUN
bv73bz62h3d	2	25	of	of	ADP
bv73bz62h3d	2	26	kawamata	kawamata	NOUN
bv73bz62h3d	2	27	about	about	ADP
bv73bz62h3d	2	28	the	the	DET
bv73bz62h3d	2	29	non	non	ADJ
bv73bz62h3d	2	30	-	-	ADJ
bv73bz62h3d	2	31	vanishing	vanish	VERB
bv73bz62h3d	2	32	of	of	ADP
bv73bz62h3d	2	33	sections	section	NOUN
bv73bz62h3d	2	34	of	of	ADP
bv73bz62h3d	2	35	line	line	NOUN
bv73bz62h3d	2	36	bundles	bundle	NOUN
bv73bz62h3d	2	37	.	.	PUNCT
bv73bz62h3d	3	1	we	we	PRON
bv73bz62h3d	3	2	show	show	VERB
bv73bz62h3d	3	3	for	for	ADP
bv73bz62h3d	3	4	certain	certain	ADJ
bv73bz62h3d	3	5	classes	class	NOUN
bv73bz62h3d	3	6	of	of	ADP
bv73bz62h3d	3	7	monomial	monomial	ADJ
bv73bz62h3d	3	8	ideals	ideal	NOUN
bv73bz62h3d	3	9	in	in	ADP
bv73bz62h3d	3	10	the	the	DET
bv73bz62h3d	3	11	polynomial	polynomial	ADJ
bv73bz62h3d	3	12	ring	ring	NOUN
bv73bz62h3d	3	13	$	$	SYM
bv73bz62h3d	3	14	k[x_1,ldots	k[x_1,ldot	NOUN
bv73bz62h3d	3	15	,	,	PUNCT
bv73bz62h3d	3	16	x_d]$	x_d]$	PROPN
bv73bz62h3d	3	17	over	over	ADP
bv73bz62h3d	3	18	a	a	DET
bv73bz62h3d	3	19	field	field	NOUN
bv73bz62h3d	3	20	of	of	ADP
bv73bz62h3d	3	21	characteristic	characteristic	ADJ
bv73bz62h3d	3	22	zero	zero	NUM
bv73bz62h3d	3	23	,	,	PUNCT
bv73bz62h3d	3	24	$	$	SYM
bv73bz62h3d	3	25	core(i)=adj(i^d)$	core(i)=adj(i^d)$	NOUN
bv73bz62h3d	3	26	if	if	SCONJ
bv73bz62h3d	3	27	and	and	CCONJ
bv73bz62h3d	3	28	only	only	ADV
bv73bz62h3d	3	29	if	if	SCONJ
bv73bz62h3d	3	30	$	$	SYM
bv73bz62h3d	3	31	core(i)$	core(i)$	PROPN
bv73bz62h3d	3	32	is	be	AUX
bv73bz62h3d	3	33	integrally	integrally	ADV
bv73bz62h3d	3	34	closed	closed	ADJ
bv73bz62h3d	3	35	.	.	PUNCT
bv73bz62h3d	4	1	in	in	ADP
bv73bz62h3d	4	2	order	order	NOUN
bv73bz62h3d	4	3	to	to	PART
bv73bz62h3d	4	4	prove	prove	VERB
bv73bz62h3d	4	5	our	our	PRON
bv73bz62h3d	4	6	main	main	ADJ
bv73bz62h3d	4	7	result	result	NOUN
bv73bz62h3d	4	8	,	,	PUNCT
bv73bz62h3d	4	9	we	we	PRON
bv73bz62h3d	4	10	further	far	ADV
bv73bz62h3d	4	11	develop	develop	VERB
bv73bz62h3d	4	12	the	the	DET
bv73bz62h3d	4	13	theory	theory	NOUN
bv73bz62h3d	4	14	of	of	ADP
bv73bz62h3d	4	15	coefficient	coefficient	ADJ
bv73bz62h3d	4	16	ideals	ideal	NOUN
bv73bz62h3d	4	17	in	in	ADP
bv73bz62h3d	4	18	regular	regular	ADJ
bv73bz62h3d	4	19	local	local	ADJ
bv73bz62h3d	4	20	rings	ring	NOUN
bv73bz62h3d	4	21	of	of	ADP
bv73bz62h3d	4	22	dimension	dimension	NOUN
bv73bz62h3d	4	23	two	two	NUM
bv73bz62h3d	4	24	and	and	CCONJ
bv73bz62h3d	4	25	study	study	VERB
bv73bz62h3d	4	26	the	the	DET
bv73bz62h3d	4	27	combinatorial	combinatorial	ADJ
bv73bz62h3d	4	28	properties	property	NOUN
bv73bz62h3d	4	29	of	of	ADP
bv73bz62h3d	4	30	the	the	DET
bv73bz62h3d	4	31	core	core	NOUN
bv73bz62h3d	4	32	of	of	ADP
bv73bz62h3d	4	33	a	a	DET
bv73bz62h3d	4	34	monomial	monomial	ADJ
bv73bz62h3d	4	35	ideal	ideal	NOUN
bv73bz62h3d	4	36	via	via	ADP
bv73bz62h3d	4	37	the	the	DET
bv73bz62h3d	4	38	symmetry	symmetry	NOUN
bv73bz62h3d	4	39	of	of	ADP
bv73bz62h3d	4	40	its	its	PRON
bv73bz62h3d	4	41	exponent	exponent	NOUN
bv73bz62h3d	4	42	set	set	NOUN
bv73bz62h3d	4	43	.	.	PUNCT