Resurgence numbers of fiber products of projective schemes

Bisui, Sankhaneel; Harbourne, Brian; Jayanthan, A. V.; Thomas, Abu Chackalamannil

doi:10.1007/s13348-020-00302-5

Cited by 8 publications

(12 citation statements)

References 21 publications

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“…In [2], the authors prove that if I and J are nonzero proper homogeneous ideals in polynomial rings with different set of variables, then max{ρ(I), ρ(J)} ≤ ρ(I + J) ≤ ρ(I) + ρ(J). It is interesting to see if any of these two inequalities can be equality.…”

Section: Resurgence Of a Homogeneous Idealmentioning

confidence: 99%

“…(1) In [2, Conjecture 3.8], the authors conjectured that there exists a homogeneous ideal I such that ρ( [2] for the definition of…”

Section: Resurgence Of a Homogeneous Idealmentioning

confidence: 99%

“…(2) For any s ≥ 1, J(G) (2s+1) = J(G)(J(G) (2) ) s . In particular, α(J(G) (2s+1) ) = α(J(G)) + sα(J(G) (2) ).…”

Section: Resurgence Of Cover Ideals Of Graphsmentioning

confidence: 99%

“…It follows from [26, Theorem 5.1] that the symbolic Rees algebra is generated in degree two. Therefore, for every s ≥ 1, we have J(G) (2s) = (J(G) (2) ) s , and…”

Section: Resurgence Of Cover Ideals Of Graphsmentioning

confidence: 99%

“…) s . Thus, for any s ≥ 1, α(J(G) (2s) ) = sα(J(G) (2) ), and α(J(G) (2s+1) ) = α(J(G)) + sα(J(G) (2) ). This proves (1) and ( 2).…”

Section: Resurgence Of Cover Ideals Of Graphsmentioning

confidence: 99%

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On the resurgence and asymptotic resurgence of homogeneous ideals

Jayanthan¹,

Kumar²,

Mukundan³

2021

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Let K be a field and R = K[x 1 , . . . , x n ]. We obtain an improved upper bound for asymptotic resurgence of squarefree monomial ideals in R. We study the effect on the resurgence when sum, product and intersection of ideals are taken. We obtain sharp upper and lower bounds for the resurgence and asymptotic resurgence of cover ideals of finite simple graphs in terms of associated combinatorial invariants. We also explicitly compute the resurgence and asymptotic resurgence of cover ideals of several classes of graphs. We characterize a graph being bipartite in terms of the resurgence and asymptotic resurgence of edge and cover ideals. We also compute explicitly the resurgence and asymptotic resurgence of edge ideals of some classes of graphs.

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Section: Resurgence Of a Homogeneous Idealmentioning

confidence: 99%

“…(1) In [2, Conjecture 3.8], the authors conjectured that there exists a homogeneous ideal I such that ρ( [2] for the definition of…”

Section: Resurgence Of a Homogeneous Idealmentioning

confidence: 99%

“…(2) For any s ≥ 1, J(G) (2s+1) = J(G)(J(G) (2) ) s . In particular, α(J(G) (2s+1) ) = α(J(G)) + sα(J(G) (2) ).…”

Section: Resurgence Of Cover Ideals Of Graphsmentioning

confidence: 99%

“…It follows from [26, Theorem 5.1] that the symbolic Rees algebra is generated in degree two. Therefore, for every s ≥ 1, we have J(G) (2s) = (J(G) (2) ) s , and…”

Section: Resurgence Of Cover Ideals Of Graphsmentioning

confidence: 99%

“…) s . Thus, for any s ≥ 1, α(J(G) (2s) ) = sα(J(G) (2) ), and α(J(G) (2s+1) ) = α(J(G)) + sα(J(G) (2) ). This proves (1) and ( 2).…”

Section: Resurgence Of Cover Ideals Of Graphsmentioning

confidence: 99%

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