About: Virtual fundamental class

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In mathematics, specifically enumerative geometry, the virtual fundamental class of a space is a replacement of the classical fundamental class in its chow ring which has better behavior with respect to the enumerative problems being considered. In this way, there exists a cycle with can be used for answering specific enumerative problems, such as the number of degree rational curves on a quintic threefold. For example, in Gromov–Witten theory, the for the class of a line in . The non-compact "smooth" component is empty, but the boundary contains maps of curves

Attributes	Values
rdfs:label	Virtual fundamental class (en)
rdfs:comment	In mathematics, specifically enumerative geometry, the virtual fundamental class of a space is a replacement of the classical fundamental class in its chow ring which has better behavior with respect to the enumerative problems being considered. In this way, there exists a cycle with can be used for answering specific enumerative problems, such as the number of degree rational curves on a quintic threefold. For example, in Gromov–Witten theory, the for the class of a line in . The non-compact "smooth" component is empty, but the boundary contains maps of curves (en)
dcterms:subject	Intersection theory
Wikipage page ID	50529391 (xsd:integer)
Wikipage revision ID	1122661530 (xsd:integer)
Link from a Wikipage to another Wikipage	Enumerative geometry Mathematics Chow ring Chow group of a stack Quintic threefold Intersection theory Euler class Intrinsic normal cone Perfect obstruction theory Deligne-Mumford stacks Gromov–Witten theory dbr:Arxiv:math/0509076 dbr:Kontsevich_moduli_space
sameAs	Virtual fundamental class Virtual fundamental class
dbp:wikiPageUsesTemplate	dbt:More_citations_needed
has abstract	In mathematics, specifically enumerative geometry, the virtual fundamental class of a space is a replacement of the classical fundamental class in its chow ring which has better behavior with respect to the enumerative problems being considered. In this way, there exists a cycle with can be used for answering specific enumerative problems, such as the number of degree rational curves on a quintic threefold. For example, in Gromov–Witten theory, the for a scheme and a class in , their behavior can be wild at the boundary, such aspg 503 having higher-dimensional components at the boundary than on the main space. One such example is in the moduli space for the class of a line in . The non-compact "smooth" component is empty, but the boundary contains maps of curves whose components consist of one degree 3 curve which contracts to a point. There is a virtual fundamental class which can then be used to count the number of curves in this family. (en)
prov:wasDerivedFrom	wikipedia-en:Virtual_fundamental_class?oldid=1122661530&ns=0
page length (characters) of wiki page	9547 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Virtual_fundamental_class
is Link from a Wikipage to another Wikipage of	Behrend function Mirror symmetry conjecture Normal cone Glossary of algebraic geometry Chow group Perfect obstruction theory Riemann–Roch-type theorem
is foaf:primaryTopic of	wikipedia-en:Virtual_fundamental_class

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