In mathematics, more specifically in algebraic geometry, the Griffiths group of a projective complex manifold X measures the difference between homological equivalence and algebraic equivalence, which are two important equivalence relations of algebraic cycles. More precisely, it is defined as where denotes the group of algebraic cycles of some fixed codimension k and the subscripts indicate the groups that are homologically trivial, respectively algebraically equivalent to zero.
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| - Griffiths group (en)
- Griffithsgrupp (sv)
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| - Inom matematiken är Griffithsgruppen av en X en grupp som mäter skillnaden mellan homologisk och algebraisk ekvivalens, två viktiga ekvivalensrelationer av . Mer precist definieras den som där betecknar gruppen av algebraiska cykler av någon fixerad kodimension k och underindexen säger att elementen i gruppen är homologiskt triviala respektive algebraiskt ekvivalenta till noll. Griffithsgruppen introducerades av , som bevisade att för en allmän femtegradskurva i (projektiva 4-rummet) är gruppen group inte en torsionsgrupp. (sv)
- In mathematics, more specifically in algebraic geometry, the Griffiths group of a projective complex manifold X measures the difference between homological equivalence and algebraic equivalence, which are two important equivalence relations of algebraic cycles. More precisely, it is defined as where denotes the group of algebraic cycles of some fixed codimension k and the subscripts indicate the groups that are homologically trivial, respectively algebraically equivalent to zero. (en)
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| - In mathematics, more specifically in algebraic geometry, the Griffiths group of a projective complex manifold X measures the difference between homological equivalence and algebraic equivalence, which are two important equivalence relations of algebraic cycles. More precisely, it is defined as where denotes the group of algebraic cycles of some fixed codimension k and the subscripts indicate the groups that are homologically trivial, respectively algebraically equivalent to zero. This group was introduced by Phillip Griffiths who showed that for a general quintic in (projective 4-space), the group is not a torsion group. (en)
- Inom matematiken är Griffithsgruppen av en X en grupp som mäter skillnaden mellan homologisk och algebraisk ekvivalens, två viktiga ekvivalensrelationer av . Mer precist definieras den som där betecknar gruppen av algebraiska cykler av någon fixerad kodimension k och underindexen säger att elementen i gruppen är homologiskt triviala respektive algebraiskt ekvivalenta till noll. Griffithsgruppen introducerades av , som bevisade att för en allmän femtegradskurva i (projektiva 4-rummet) är gruppen group inte en torsionsgrupp. (sv)
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