Embedded Files
(01:17) Curves Chapter 1.pdfChapter 1 Divisors & linear series
Chapter 1 Divisors & linear series
Michael: divisors, line bundles, linear series, morphism into projective space.
(01:22) Curves Chapter 2.pdfChapter 2 Riemann-Roch & Riemann-Hurwitz
Chapter 2 Riemann-Roch & Riemann-Hurwitz
Haocheng: Riemann-Roch for curves and surfaces, Riemann-Hurwitz
(01:24) Curves Chapters 3 & 4.pdfChapters 3 & 4 Curves of genus 0, plane curves, curves of genus 1
Chapters 3 & 4 Curves of genus 0, plane curves, curves of genus 1
Michael: rational normal curves, linear series on plane curves, group law on cubics, Cayley-Banarach, maps from elliptic to projective spaces.
(01:29) Jacobians.pdfChapter 5 Jacobians
Chapter 5 Jacobians
Ethan: Analytic construction of Jacobians, the g+3 theorem.
(01:31) Hyperelliptic Curves and Their Group Law.pdfHyperelliptic Curves and Their Group Law
Hyperelliptic Curves and Their Group Law
Bryan B.: hyperelliptic curves, the canonical morphism, group laws on symmetric products.
(02:05) Castelnuovo-Severi.pdfDegree d points, Castelnuovo-Severi, and dynatomic modular curves
Degree d points, Castelnuovo-Severi, and dynatomic modular curves
Alex G.: Castelnuovo-Severi bound, degree d rational points on curves, and dynamics on curves.
(02:19) Stable Reduction.pdfModuli of curves: Stable Reduction
Moduli of curves: Stable Reduction
Arkamouli: Intro to moduli of curves, stable reduction
(02:22) Moduli of Elliptic Curves and Modular Forms.pdfModuli of curves: M11-bar and modular forms
Moduli of curves: M11-bar and modular forms
Davide: Moduli of elliptic curves, modular forms, and line bundles over M11 bar.
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