TY - JOUR
T1 - Refined elliptic tropical enumerative invariants
AU - Schroeter, Franziska
AU - Shustin, Eugenii
N1 - Publisher Copyright:
© 2018, Springer New York LLC. All rights reserved.
PY - 2018/4/18
Y1 - 2018/4/18
N2 - We suggest a new refined (i.e., depending on a parameter) tropical enumerative invariant of toric surfaces. This is the first known enumerative invariant that counts tropical curves of positive genus with marked vertices. Our invariant extends the refined rational broccoli invariant invented by L. Göttsche and the first author, though there is a serious difference between the invariants: our elliptic invariant counts weights assigned partly to individual tropical curves and partly to collections of tropical curves, and our invariant is not always multiplicative over the vertices of the counted tropical curves as was the case for other known tropical enumerative invariants of toric surfaces. As a consequence we define elliptic broccoli curves and elliptic broccoli invariants as well as elliptic tropical descendant invariants for any toric surface.
AB - We suggest a new refined (i.e., depending on a parameter) tropical enumerative invariant of toric surfaces. This is the first known enumerative invariant that counts tropical curves of positive genus with marked vertices. Our invariant extends the refined rational broccoli invariant invented by L. Göttsche and the first author, though there is a serious difference between the invariants: our elliptic invariant counts weights assigned partly to individual tropical curves and partly to collections of tropical curves, and our invariant is not always multiplicative over the vertices of the counted tropical curves as was the case for other known tropical enumerative invariants of toric surfaces. As a consequence we define elliptic broccoli curves and elliptic broccoli invariants as well as elliptic tropical descendant invariants for any toric surface.
UR - http://www.scopus.com/inward/record.url?scp=85046021703&partnerID=8YFLogxK
U2 - 10.1007/s11856-018-1680-6
DO - 10.1007/s11856-018-1680-6
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AN - SCOPUS:85046021703
SN - 0021-2172
VL - 225
SP - 817
EP - 869
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -