Meromorphic nearby cycle functors and monodromies of meromorphic functions (with Appendix by T. Saito)

Nguyen, Tat Thang; Takeuchi, Kiyoshi

doi:10.1007/s13163-022-00431-4

Cited by 5 publications

(8 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By the proof of Theorem 1.1 and the correspondence , the Bernstein–Sato polynomial of coincides with . This, in particular, implies that we have Note also that for the -module in the proof of Theorem 1.1, we have an isomorphism and the nearby cycle sheaf coincides with the meromorphic nearby cycle introduced in [29] up to some shift. Assume first that .…”

Section: Proof Of Theorem 14mentioning

confidence: 61%

“…Combining Theorem 1.4 with the results in [29] and [32], one may formulate a monodromy conjecture for rational functions, like the original one in [11]. For previous works in this direction, see, for example, [14] and [38].…”

Section: Introductionmentioning

confidence: 89%

“…Note that if in a coordinate system F and G depend on separated variables, we can easily see that our b mero f,m (s) coincides with the bfunction b F (s) of the holomorphic function F. At the moment, except for such trivial cases, we cannot calculate b mero f,m (s) explicitly. Instead, by [29,Th. 3.3 and Cor.…”

Section: §1 Introductionmentioning

confidence: 98%

“…At the moment, except for such trivial cases, we cannot calculate explicitly. Instead, by [29, Th. 3.3 and Cor.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On a Bernstein–sato Polynomial of a Meromorphic Function

Takeuchi

2023

Nagoya Math. J.

Self Cite

View full text Add to dashboard Cite

We define Bernstein–Sato polynomials for meromorphic functions and study their basic properties. In particular, we prove a Kashiwara–Malgrange-type theorem on their geometric monodromies, which would also be useful in relation with the monodromy conjecture. A new feature in the meromorphic setting is that we have several b-functions whose roots yield the same set of the eigenvalues of the Milnor monodromies. We also introduce multiplier ideal sheaves for meromorphic functions and show that their jumping numbers are related to our b-functions.

show abstract

Section: Proof Of Theorem 14mentioning

confidence: 61%

Section: Introductionmentioning

confidence: 89%

Section: §1 Introductionmentioning

confidence: 98%

“…At the moment, except for such trivial cases, we cannot calculate explicitly. Instead, by [29, Th. 3.3 and Cor.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On a Bernstein–sato Polynomial of a Meromorphic Function

Takeuchi

2023

Nagoya Math. J.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The definition of zeta function in Definition 5.1, page 22 in [1] (formula (5.3)) is corrected as follow (the exponent of L is replaced by −rmn):…”

mentioning

confidence: 99%

Correction to: Meromorphic nearby cycle functors and monodromies of meromorphic functions (with Appendix by T. Saito)

Nguyen

Takeuchi

2022

Rev Mat Complut

Self Cite

View full text Add to dashboard Cite

show abstract

Newton transformations and motivic invariants at infinity of plane curves

Cassou-Noguès

Raibaut

2021

Math. Z.

View full text Add to dashboard Cite

Let P and Q be two polynomials in two variables with coefficients in an algebraic closed field of characteristic zero. We consider the rational function f = P/Q. For an indeterminacy point x of f and a value c, we compute the motivic Milnor fiber S f,x,c in terms of some motives associated to the faces of the Newton polygons appearing in the Newton algorithms of P − cQ and Q at x, without any condition of non-degeneracy or convenience. In the complex setting, assuming for any (a, b) ∈ C 2 that x is smooth or an isolated critical point of aP + bQ, and the curves P = 0 and Q = 0 do not have common irreducible component, we prove that the topological bifurcation set B top f,x is equal to the motivic bifurcation set B mot f,x and they are computed from the Newton algorithm.

show abstract

Meromorphic nearby cycle functors and monodromies of meromorphic functions (with Appendix by T. Saito)

Cited by 5 publications

References 43 publications

On a Bernstein–sato Polynomial of a Meromorphic Function

On a Bernstein–sato Polynomial of a Meromorphic Function

Correction to: Meromorphic nearby cycle functors and monodromies of meromorphic functions (with Appendix by T. Saito)

Newton transformations and motivic invariants at infinity of plane curves

Contact Info

Product

Resources

About