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FIELD GUIDE
Algebraic and complex geometry
Official catalogue 032–069.
Open the official catalogue · p. 5 ↗Read the results and proof connections of five manuscripts on subadditivity, whole-fiber variation, additivity, and semiampleness.
All 5 overviews availableThe catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.
Explore the synthesis and connectionsA guide to manuscripts on abundance and good minimal models, organized by hypotheses, conclusions, and arguments.
All 14 overviews availableThe catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.
Explore the synthesis and connectionsFollow four proofs of models with fixed nef data, projective and Kähler numerical semiampleness, and minimal models in numerical dimension one.
All 4 overviews availableThe catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.
Explore the synthesis and connectionsFollow two proofs from the fourfold hypersurface reduction to the volume gap and equality classification in every dimension, with global consequences.
All 2 overviews availableThe catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.
Explore the synthesis and connectionsFollow exponential minimization and local lifting through the claimed proof of Fujita’s freeness conjecture.
Proof overview availableThe catalogue guide leads to the article, its external inputs, and the bilingual PDF editions.
Open the catalogue guideFollow four proofs of the strict plane Nagata inequality and maximal multipoint Seshadri constants on surfaces, in higher dimensions, and in positive characteristic.
All 4 overviews availableThe catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.
Explore the synthesis and connectionsFollow local operations, period cases, and convex approximation to the Oka property of K3 surfaces and its consequences.
Proof overview availableThe catalogue guide leads to the article, its external inputs, and the bilingual PDF editions.
Open the catalogue guideFollow two constructions of projective varieties whose universal covers fail holomorphic convexity: a fourfold with large fundamental group and a surface with chains of rational curves.
All 2 overviews availableThe catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.
Explore the synthesis and connectionsConnects a symmetric-power filtration from two quotients to an invariant-measure obstruction from the graph identities.
Proof overview availableThe catalogue guide leads to the article, its external inputs, and the bilingual PDF editions.
Open the catalogue guideFollow disc variations to canonical ampleness and its consequences for global generation and finite covers.
Proof overview availableThe catalogue guide leads to the article, its external inputs, and the bilingual PDF editions.
Open the catalogue guideFollow two proofs separating integrability of a prescribed tangent splitting from product decompositions of the universal cover or the manifold itself.
All 2 overviews availableThe catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.
Explore the synthesis and connectionsFollow three proofs linking ordinary fundamental groups of special varieties, linear images for open varieties, and the passage to root orbifolds.
All 3 overviews availableThe catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.
Explore the synthesis and connectionsAfter the square-zero-divisor case, passes from relative Chern classes on the cyclic cover through sections and compact components to a rational-curve count and a shell criterion.
Proof overview availableThe catalogue guide leads to the article, its external inputs, and the bilingual PDF editions.
Open the catalogue guideFollow point descendants, quantum multiplication, and minimal rational curves through the generalized Mukai inequality and its equality case.
Proof overview availableThe catalogue guide leads to the article, its external inputs, and the bilingual PDF editions.
Open the catalogue guideFollow characteristic-number constraints on minimal rational curves and VMRT recognition through the classification of Fano sixfolds with nef tangent bundle.
Proof overview availableThe catalogue guide leads to the article, its external inputs, and the bilingual PDF editions.
Open the catalogue guideFollow seven proofs connecting anticanonical nonvanishing with invariant indices, metric descent, and invariant sections.
All 7 overviews availableThe catalogue synthesis connects the results, proof strategies, and theorems used across these manuscripts.
Explore the synthesis and connections