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Birational geometry of symplectic resolutions of nilpotent orbits II

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Yoshinori Namikawa

Algebraic Geometry · Submitted 20 Aug 2004

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Then we prove that all symplectic resolution of the nilpotent closure are Springer resolutions with $P$ which are equivalent to $P_0$.

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arXiv IDmath/0408274 (version 2)
Pith IDD3WVKLD5, Pith's permanent record of this paper and its review
CitationYoshinori Namikawa. "Birational geometry of symplectic resolutions of nilpotent orbits II." arXiv:math/0408274 (2004). https://pith.science/paper/D3WVKLD5
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,143 input tokens.

What the abstract itself states, as probabilities: claims first 0.12 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.45 · compares with prior results 0.73 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this paper we shall study symplectic resolutions of a nilpotent orbit closure of a complex simple Lie algebra \g. We shall introduce an equivalence relation in the set of parabolic subgroups of $G$ in terms of marked Dynkin diagrams. We start with a nilpotent orbit closure which admits a Springer resolution with a parabolic subgroup $P_0$ of $G$. Then we prove that all symplectic resolution of the nilpotent closure are Springer resolutions with $P$ which are equivalent to $P_0$. Here all symplectic resolutions are connected by Mukai flops. We need three types of Mukai flops (types A, D and E_6) in connecting symplectic resolutions. In particular, Mukai flops of type E_6 are new. All arguments of Part I : math.AG/0404072 which use flags, are replaced by those which use only Dynkin diagrams.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we shall study symplectic resolutions of a nilpotent orbit closure of a complex simple Lie algebra \g. contribution 0.77 0.76 0.04 asserted 0.74
s1 We shall introduce an equivalence relation in the set of parabolic subgroups of $G$ in terms of marked Dynkin diagrams. contribution 0.80 0.92 0.04 asserted 0.97
s2 We start with a nilpotent orbit closure which admits a Springer resolution with a parabolic subgroup $P_0$ of $G$. background 0.56 0.21 0.03 asserted 0.92
s3 Then we prove that all symplectic resolution of the nilpotent closure are Springer resolutions with $P$ which are equivalent to $P_0$. result 0.99 0.92 0.79 asserted 1.00
s4 Here all symplectic resolutions are connected by Mukai flops. result 0.96 0.81 0.13 asserted 1.00
s5 We need three types of Mukai flops (types A, D and E_6) in connecting symplectic resolutions. result 0.50 0.81 0.06 asserted 1.00
s6 In particular, Mukai flops of type E_6 are new. contribution 0.71 0.80 0.05 asserted 1.00
s7 All arguments of Part I : math.AG/0404072 which use flags, are replaced by those which use only Dynkin diagrams. method 0.63 0.83 0.03 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper we shall study symplectic resolutions of a nilpotent orbit closure of a complex simple Lie algebra \g. We shall introduce an equivalence relation in the set of parabolic subgroups of $G$ in terms of marked Dynkin diagrams. We start with a nilpotent orbit closure which admits a Springer resolution with a parabolic subgroup $P_0$ of $G$. Then we prove that all symplectic resolution of the nilpotent closure are Springer resolutions with $P$ which are equivalent to $P_0$. Here all symplectic resolutions are connected by Mukai flops. We need three types of Mukai flops (types A, D and E_6) in connecting symplectic resolutions. In particular, Mukai flops of type E_6 are new. All arguments of Part I : math.AG/0404072 which use flags, are replaced by those which use only Dynkin diagrams.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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