Example：10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502
Monodromy of rational curves on toric surfaces Journal of Topology (IF1.582), Pub Date : 2020-10-23, DOI: 10.1112/topo.12171 Lionel Lang
For an ample line bundle on a complete toric surface , we consider the subset of irreducible, nodal, rational curves contained in the smooth locus of . We study the monodromy map from the fundamental group of to the permutation group on the set of nodes of a reference curve . We identify a certain obstruction map defined on the set of nodes of and show that the image of the monodromy is exactly the group of deck transformations of , provided that is sufficiently big (in the sense we make precise below). Along the way, we construct a handy tool to compute the image of the monodromy for any pair . Eventually, we present a family of pairs with small and for which the image of the monodromy is strictly smaller than expected.