Cohomological support loci of varieties of Albanese fiber dimension one

Hao Sun; Zhi Jiang

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Cohomological support loci of varieties of Albanese fiber dimension one

Zhi Jiang, Hao Sun

Algebraic Geometry · Submitted 12 Sep 2011

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

The authors' main claim We prove that the translates through 0 of all components of $V^0(\omega_X)$ generate $\Pic^0(X)$.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,481 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Let $X$ be a smooth projective variety of Albanese fiber dimension 1 and of general type. We prove that the translates through 0 of all components of $V^0(\omega_X)$ generate $\Pic^0(X)$. We then study the pluricanonical maps of $X$. We show that $|4K_X|$ induces a birational map.

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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	Let $X$ be a smooth projective variety of Albanese fiber dimension 1 and of general type.	background 0.98	0.08	0.02	asserted 0.82
s1	We prove that the translates through 0 of all components of $V^0(\omega_X)$ generate $\Pic^0(X)$.	result 0.99	0.96	0.65	asserted 1.00
s2	We then study the pluricanonical maps of $X$.	contribution 0.99	0.81	0.03	unclear 0.57
s3	We show that $\|4K_X\|$ induces a birational map.	result 1.00	0.95	0.30	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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arXiv listing abstract v3

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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

Let $X$ be a smooth projective variety of Albanese fiber dimension 1 and of general type. We prove that the translates through 0 of all components of $V^0(\omega_X)$ generate $\Pic^0(X)$. We then study the pluricanonical maps of $X$. We show that $|4K_X|$ induces a birational map.

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What this paper does with the arXiv papers it cites

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

What it cites · 7 sentences without a confident label

Uses the method or tool of 2 papers

We employ a trick of Tirabassi ( [ref] ) to show that Under the setting of diagram ([ref]), we assume moreover that 1) $2K_F$ is globally generated; 2) the translates through $0$ of all irreducible components of $V^0(ω_X)$ generate $^0(X)$; then there exists an open dense subset $U$ of $X$ such that for any $x∈U$, the sheaf [equation] is $M$-regular.

On the tetracanonical map of varieties of general type and maximal Albanese dimension · Pluircanonical maps · 1.00
One might want to mimic the argument in [ref] .

On the Iitaka fibration of varieties of maximal Albanese dimension · Pluircanonical maps · 0.88

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