Enumerating pencils with moving ramification on curves
نویسندگان
چکیده
We consider the general problem of enumerating branched covers projective line from a fixed curve subject to ramification conditions at possibly moving points. Our main computations are in genus 1; theory limit linear series allows one reduce this case. first obtain simple formula for weighted count pencils on elliptic E E , where base-points allowed. then deduce, using an inclusion-exclusion procedure, formulas numbers maps E right-arrow double-struck upper P Superscript 1"> ? P 1 encoding="application/x-tex">E\to \mathbb {P}^1 with conditions. A striking consequence is invariance these counts under certain involution. results generalize work Harris, Logan, Osserman, and Farkas-Moschetti-Naranjo-Pirola.
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2021
ISSN: ['1534-7486', '1056-3911']
DOI: https://doi.org/10.1090/jag/776