TY - JOUR
T1 - Tangency quantum cohomology
AU - Kock, Joachim
PY - 2004/1
Y1 - 2004/1
N2 - Let X be a smooth projective variety. Using modified psi classes on the stack of genus-zero stable maps to X, a new associative quantum product is constructed on the cohomology space of X. When X is a homogeneous variety, this structure encodes the characteristic numbers of rational curves in X, and specialises to the usual quantum product upon resetting the parameters corresponding to the modified psi classes. For X= ℙ2, the product is equivalent to that of the contact cohomology of Ernström and Kennedy.
AB - Let X be a smooth projective variety. Using modified psi classes on the stack of genus-zero stable maps to X, a new associative quantum product is constructed on the cohomology space of X. When X is a homogeneous variety, this structure encodes the characteristic numbers of rational curves in X, and specialises to the usual quantum product upon resetting the parameters corresponding to the modified psi classes. For X= ℙ2, the product is equivalent to that of the contact cohomology of Ernström and Kennedy.
KW - Enumerative geometry
KW - Gromov-Witten invariants
KW - Quantum cohomology
UR - https://www.scopus.com/pages/publications/43449103622
U2 - 10.1112/S0010437X03000101
DO - 10.1112/S0010437X03000101
M3 - Article
AN - SCOPUS:43449103622
SN - 0010-437X
VL - 140
SP - 165
EP - 178
JO - Compositio Mathematica
JF - Compositio Mathematica
IS - 1
ER -