On Constraints Imposed by Independent Gonal Morphisms for a Curve
 Title:
 On Constraints Imposed by Independent Gonal Morphisms for a Curve
 Author(s):
 Jiang, Feiqi
 Thesis Advisor(s):
 de Jong, Aise Johan
 Date:
 2018
 Type:
 Theses
 Degree:
 Ph.D., Columbia University
 Department(s):
 Mathematics
 Persistent URL:
 https://doi.org/10.7916/D81R86XJ
 Abstract:
 In this thesis, we explore the restrictions imposed on the genus of a smooth curve $X$ which possesses at least three independent gonal morphisms to $\Pp^1$. We will prove a sharp lower bound on the dimension of global sections given by the sum of the divisors for the gonal morphisms. This inequality will provide an upper bound on the genus of a curve with the described properties. By considering the birational image of $X$ in $\Pp^1 \times \Pp^1 \times \Pp^1$ under the product of three pairwise independent morphisms, we observe that the boundary case for the previously mentioned inequality is closely related to the case where the image of $X$ is contained in a type 111 surface. Motivated by this phenomenon, we examine the constraints on the arithmetic genus of an irreducible curve in $\Pp^1 \times \Pp^1 \times \Pp^1$ whose natural projections are pairwise independent and all have degree 7.
 Subject(s):
 Mathematics
Curves
Riemann surfaces
Geometry
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 Suggested Citation:
 Feiqi Jiang, 2018, On Constraints Imposed by Independent Gonal Morphisms for a Curve, Columbia University Academic Commons, https://doi.org/10.7916/D81R86XJ.