A young person's guide to mixed Hodge modules

Morihiko Saito

RECORD

A young person's guide to mixed Hodge modules

Morihiko Saito

Algebraic Geometry · Submitted 2 May 2016

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

The authors' main claim We give a rather informal introduction to the theory of mixed Hodge modules for young mathematicians.

how it is stated · asserted 0.95 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,570 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.39 · human participants 0.03 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.02 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v5. Results and the main claim are underlined; show every role.

We give a rather informal introduction to the theory of mixed Hodge modules for young mathematicians.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We give a rather informal introduction to the theory of mixed Hodge modules for young mathematicians.	contribution 1.00	0.84	0.17	asserted 0.95

What kind of paper the classifier reports this is: review 0.97 · evidence from argument 0.70.

What was examined, and what was not

sources read

arXiv listing abstract v5

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

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

We give a rather informal introduction to the theory of mixed Hodge modules for young mathematicians.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

13 arXiv papers cite this in 19 sentences

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

Papers citing it · 12 sentences without a confident label

Cites it as background 7 papers

Here $d_XXd_Y-1$, and $$ is the dual functor for filtered left $$-modules (which is defined in a compatible way with the one for filtered right $$-modules, see for instance [ref] , [ref] , [ref] ).

Hirzebruch-Milnor classes of hypersurfaces with nontrivial normal bundles and applications to higher du Bois and rational singularities · Introduction · 0.81
The Hodge-theoretic background includes the theory of degenerations and limiting mixed Hodge structures [ref] , together with Saito's mixed-Hodge-module formalism [ref] .

From Finite-Node Conifold Geometry to BPS Structures III: Mediated Triangle Transport and Graded Interaction Data · Related work · 1.00
Let $MHM(_β(X))$ be the abelian category of polarized mixed Hodge modules on $_β(X)$, whose basics we refer to [ref] .

Gopakumar-Vafa invariants via vanishing cycles · $sl_2 ×sl_2$-action · 1.00

What it cites · 7 sentences without a confident label

Uses the method or tool of 1 paper

Theorem (2.4) then follows from the theory of bi-graded Hodge structures of Lefschetz type as in the proof of [ref] (see also [ref] where a slightly better explanation is given).

Monodromy Filtration and Positivity · Introduction · 0.85

Cites as background 9 papers

Concerning Hirzebruch characteristic classes, see [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , etc.

Hirzebruch-Milnor classes and Steenbrink spectra of certain projective hypersurfaces · Introduction · 0.98
Concerning Hirzebruch characteristic classes, see [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , etc.

Characteristic classes of mixed Hodge modules and applications · Introduction · 0.98
Concerning Hirzebruch characteristic classes, see [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , etc.

Spectral Hirzebruch-Milnor classes of singular hypersurfaces · Introduction · 0.98

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.