TY - JOUR
T1 - On refined count of rational tropical curves
AU - Shustin, Eugenii
N1 - Publisher Copyright:
© 2020, Homology, Homotopy and Applications. All rights reserved.
PY - 2020
Y1 - 2020
N2 - We address the problem of existence of refined (i.e., depending on a formal parameter) tropical enumerative invariants, and we present two new examples of a refined count of rational marked tropical curves. One of the new invariants counts plane rational tropical curves with an unmarked vertex of arbitrary valency. It was motivated by the tropical enumeration of plane cuspidal tropical curves given by Y. Ganor and the author, which naturally led to consideration of plane tropical curves with an unmarked four-valent vertex. Another refined invariant counts rational tropical curves of a given degree in the Euclidean space of arbitrary dimension matching specific constraints, which make the spacial refined invariant similar to known planar invariants.
AB - We address the problem of existence of refined (i.e., depending on a formal parameter) tropical enumerative invariants, and we present two new examples of a refined count of rational marked tropical curves. One of the new invariants counts plane rational tropical curves with an unmarked vertex of arbitrary valency. It was motivated by the tropical enumeration of plane cuspidal tropical curves given by Y. Ganor and the author, which naturally led to consideration of plane tropical curves with an unmarked four-valent vertex. Another refined invariant counts rational tropical curves of a given degree in the Euclidean space of arbitrary dimension matching specific constraints, which make the spacial refined invariant similar to known planar invariants.
KW - Plane tropical curve
KW - Rational tropical curve
KW - Refined enumerative invariants
KW - Spacial tropical curve
KW - Tropical enumerative geometry
UR - http://www.scopus.com/inward/record.url?scp=85096909410&partnerID=8YFLogxK
U2 - 10.4310/PAMQ.2020.v16.n4.a5
DO - 10.4310/PAMQ.2020.v16.n4.a5
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AN - SCOPUS:85096909410
SN - 1558-8599
VL - 16
SP - 1027
EP - 1052
JO - Pure and Applied Mathematics Quarterly
JF - Pure and Applied Mathematics Quarterly
IS - 4
ER -