6533b85cfe1ef96bd12bc182

RESEARCH PRODUCT

Effectively Computing Integral Points on the Moduli of Smooth Quartic Curves

Ariyan Javanpeykar

subject

Pure mathematicsConjectureMathematics - Number TheoryMathematics::Commutative AlgebraDegree (graph theory)Mathematics::Number TheoryGeneral Mathematics010102 general mathematics01 natural sciencesModuliMathematics - Algebraic GeometryMathematics::Algebraic GeometryQuartic function0103 physical sciencesFOS: MathematicsNumber Theory (math.NT)010307 mathematical physics0101 mathematicsAlgebraic Geometry (math.AG)Mathematics

description

We prove an effective version of the Shafarevich conjecture (as proven by Faltings) for smooth quartic curves. To do so, we establish an effective version of Scholl's finiteness result for smooth del Pezzo surfaces of degree at most four.

yearjournalcountryeditionlanguage
2016-04-18The Quarterly Journal of Mathematics
https://doi.org/10.1093/qmath/haw043