Statements (59)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:variety_show
|
| gptkbp:are |
used in string theory
a subject of interest in both mathematics and theoretical physics a key area of research in the field of algebraic geometry. a central topic in modern algebraic geometry a key concept in the theory of algebraic surfaces a special case of Mori dream spaces connected to minimal models examples of varieties with ample canonical bundle generalizations of toric varieties important in the context of algebraic cycles important in the context of algebraic topology important in the study of birational geometry often classified by their singularities often studied in relation to their singularities often used in the context of mirror symmetry often used in the context of rationality questions related to the Minimal Model Program related to the theory of moduli spaces used in the study of deformation theory often studied in relation to their deformation spaces a focus of research in higher-dimensional algebraic geometry |
| gptkbp:associated_with |
projective geometry
|
| gptkbp:can |
non-trivial automorphisms
rational curves extremal rays finite automorphism groups special fibers special geometric properties various types of singularities |
| gptkbp:can_be |
smooth or singular
|
| gptkbp:can_be_used_in |
projective space
classification of algebraic varieties |
| gptkbp:can_be_used_to |
construct examples of higher-dimensional varieties
|
| gptkbp:characteristic |
positive curvature
|
| gptkbp:connects |
the study of algebraic groups
|
| gptkbp:constructed_in |
toric varieties
|
| gptkbp:dimensions |
n
|
| gptkbp:example |
projective spaces
del Pezzo surfaces quadrics |
| gptkbp:has_role |
mirror symmetry
|
| gptkbp:have |
rational points
ample anticanonical bundle non-negative Kodaira dimension |
| https://www.w3.org/2000/01/rdf-schema#label |
Fano varieties
|
| gptkbp:importance |
in algebraic geometry
|
| gptkbp:is_analyzed_in |
cohomological methods
|
| gptkbp:is_associated_with |
the study of rationality problems
|
| gptkbp:is_characterized_by |
their intersection numbers
their intersection theory |
| gptkbp:is_defined_by |
Fano condition
|
| gptkbp:is_described_as |
their defining equations
|
| gptkbp:is_studied_in |
their birational properties
|
| gptkbp:named_after |
Gino Fano
|
| gptkbp:related_to |
gptkb:Kähler_manifold
|
| gptkbp:scientific_classification |
their Picard group
|
| gptkbp:bfsParent |
gptkb:Calabi-Yau_manifold
|
| gptkbp:bfsLayer |
6
|