タグ一覧 | Geometry Paper Digest

特異点・特異性

Singularities
Singular spaces, pairs, or maps and their singularity classes, local invariants, resolutions, or degenerations are central.
46件
双有理幾何

Birational geometry
Birational models, maps, boundedness, contractions, flops, or birational invariants are central.
25件
極小モデル・プログラム

Minimal model program
MMP operations or its cone, contraction, abundance, or termination framework drive the result.
13件
正値性

Positivity
Positivity of line/vector bundles, sheaves, divisors, currents, or cohomology classes (ample, nef, big, pseudo-effective, Nakano/Griffiths positivity) is a main question or criterion.
44件
正標数

Positive characteristic
Positive characteristic, Frobenius methods, F-singularities, F-splitting, or reduction mod $p$ is a central setting or method.
9件
ベクトル束・層

Vector bundles and sheaves
Bundles, coherent/reflexive sheaves, their moduli/invariants, or bundle-valued equations are principal objects.
58件
モジュライ・族

Moduli and families
Construction, geometry, compactification, boundedness, deformation, or variation of moduli spaces/families is central.
24件
束・層の安定性

Stability of bundles and sheaves
Slope, Gieseker, Higgs-sheaf, or related stability and Harder–Narasimhan structures are central.
26件
K安定性

K-stability
K-, Ding-, or valuative stability of polarized/log/Fano objects is a main notion or conclusion.
15件
Hermite–Einstein計量

Hermite–Einstein metrics
Hermite–Einstein/Hermitian–Einstein metrics, HYM equations/flows, or the Kobayashi–Hitchin correspondence are central objects or conclusions.
9件
ケーラー・アインシュタイン計量

Kähler–Einstein metrics
Existence, uniqueness, degeneration, deformation, or geometry of Kähler–Einstein metrics is central.
7件
cscK・extremal Kähler計量

cscK and extremal Kähler metrics
Constant-scalar-curvature Kähler, extremal Kähler, weighted cscK/extremal metrics, or their existence, limits, and moduli are central.
10件
ケーラー・リッチ流・ソリトン

Kähler–Ricci flow and solitons
Include flow-only papers when evolution or long-time behavior is central; soliton-only papers for shrinking, steady, or expanding Kähler–Ricci solitons; and papers centrally relating flow limits to solitons.
9件
曲率幾何

Curvature geometry
Riemannian/Hermitian curvature, Ricci/scalar/sectional curvature, or curvature connections are central hypotheses or conclusions.
42件
非コンパクトKähler幾何

Noncompact Kähler geometry
Completeness, geometry at infinity, volume growth, exhaustion functions, splitting/structure theory, or function theory on a complete noncompact Kähler manifold is essential to the main hypotheses or conclusions.
5件
距離空間極限・Gromov–Hausdorff幾何

Metric limits and Gromov–Hausdorff geometry
Gromov–Hausdorff/measured convergence, Ricci limit spaces, metric degeneration or compactness, tangent cones, or Cheeger–Colding-type theory is a central structure.
7件
ファノ多様体

Fano varieties
Fano, weak Fano, log Fano, or del Pezzo geometry is a principal object.
25件
カラビ・ヤウ幾何

Calabi–Yau geometry
Calabi–Yau varieties/manifolds, pairs, fibrations, or their defining trivial-canonical geometry are central.
8件
ハイパーケーラー幾何

Hyperkähler geometry
Hyperkähler/irreducible holomorphic symplectic manifolds, fibrations, sheaves, or Torelli phenomena are central.
6件
ホッジ理論

Hodge theory
Hodge structures, variations, period/Torelli maps, Hodge bundles, or Hodge-theoretic invariants are central.
10件
ヒッグス束・非可換ホッジ理論

Higgs bundles and nonabelian Hodge theory
Higgs bundles/pairs, Hitchin systems, harmonic bundles, or nonabelian Hodge correspondences are central.
13件
葉層構造

Foliations
Algebraic, holomorphic, or transverse foliations and their singularities/MMP/curvature are principal objects.
10件
多重ポテンシャル論

Pluripotential theory
Plurisubharmonic/quasi-psh potentials, non-pluripolar products, complex Monge–Ampère/Hessian equations, or weak positive-current methods are central objects or frameworks.
7件
複素Monge–Ampère方程式

Complex Monge–Ampère equations
Existence, uniqueness, regularity, degeneracy, or Monge–Ampère measures for complex Monge–Ampère equations—or genuinely allied complex Hessian equations—is central, including when solving the equation drives a geometric construction.
3件
L²法

L² methods
Hörmander-type $L^2$ estimates, $L^2$ solutions of $\bar\partial$, Ohsawa–Takegoshi-type extension, or $L^2$ Hodge theory are principal proof methods.
5件
乗数イデアル・拡張定理

Multiplier ideals and extension theorems
Multiplier/adjoint ideals, Nadel-type techniques, Ohsawa–Takegoshi extension, extension of pluricanonical sections, or Siu/Takayama/Păun-type extension is a main result or principal proof method.
4件
複素解析空間

Complex analytic spaces
Complex/normal/singular analytic spaces, modifications, exceptional sets, or coherent analytic sheaves are central objects.
9件
Stein幾何・Levi問題

Stein geometry and the Levi problem
Stein manifolds/spaces, the Levi problem, holomorphic convexity, pseudoconvex exhaustion, weakly 1-complete or $q$-complete spaces, Remmert reduction, exceptional sets in a 1-convex setting, or Steinness criteria are central.
5件
Oka理論

Oka theory
Oka manifolds/principles, ellipticity or subellipticity, holomorphic flexibility, or Oka-type approximation/interpolation are central.
3件
双曲性

Hyperbolicity
Kobayashi/Brody/Kähler hyperbolicity, hyperbolicity indices, or algebraic/pseudo-hyperbolicity is central.
8件
基本群

Fundamental groups
Fundamental groups, their algebraic/analytic structure, virtual properties, simple connectedness, or Shafarevich-type constructions are central.
9件
一意化

Uniformization
A ball/locally symmetric quotient characterization, uniformization theorem, or geometric classification by a universal model is central.
6件
Chern類・Chern数

Chern classes and Chern numbers
Chern classes/numbers, first or second Chern classes, Miyaoka–Yau-type Chern-number inequalities, orbifold/Q-Chern classes, or a geometric characterization by Chern classes are central invariants or conclusions.
11件
代数的サイクル・数え上げ幾何

Algebraic cycles and enumerative geometry
Chow/cycle groups, regulators, enumerative invariants, or counting problems are central.
5件
シンプレクティック・接触幾何

Symplectic and contact geometry
Symplectic/almost-Kähler structures, holomorphic symplectic moduli, or contact manifolds are principal objects.
9件
CR幾何

CR geometry
CR structures, invariants, embeddings, normal forms, or pseudohermitian geometry are central.
3件
トーリック幾何

Toric geometry
Toric varieties/manifolds, polytopes, fans, or torus-equivariant structures drive the result.
12件