Gonality of an algebraic curve

Claire Voisin: Gonality and zero-cycles of abelian varieties

Abstract: The gonality of a variety is defined as the minimal gonality of curve sitting in the variety. We prove that the gonality of a very general abelian variety of dimension g goes to infinity with g. We use for this a (straightforward) generalization of a method due to Pirola that we

From playlist Algebraic and Complex Geometry

Syzygies, gonality and symmetric products of curves - Robert Lazarsfeld

Robert Lazarsfeld Stony Brook University April 14, 2015 In the mid 1980s, Mark Green and I conjectured that one could read off the gonality of an algebraic curve CC from the syzygies among the equations defining any one sufficiently positive embedding of CC. Ein and I recently noticed that

From playlist Mathematics

Ariyan Javanpeykar: Arithmetic and algebraic hyperbolicity

Abstract: The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have onl

From playlist Algebraic and Complex Geometry

Weil conjectures 6: etale cohomology of a curve

We give an overview of how to calculate the etale cohomology of a nonsinguar projective curve over an algebraically closed field with coefficients Z/nZ with n invertible. We simply assume a lot of properties of etale cohomology without proving (or even defining) them.

From playlist Algebraic geometry: extra topics

Low degree points on curves. - Vogt - Workshop 2 - CEB T2 2019

Isabel Vogt (MIT) / 27.06.2019 Low degree points on curves. In this talk we will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris–S

From playlist 2019 - T2 - Reinventing rational points

Tangents to Parametric Curves (New) | Algebraic Calculus One | Wild Egg

Tangents are an essential part of the differential calculus. Here we introduce these important lines which approximate curves at points in an algebraic fashion -- finessing the need for infinite processes to support takings of limits. We begin by a discussion of tangents historically, espe

From playlist Algebraic Calculus One

Hannah Larson - A refined Brill-Noether theory over Hurwitz spaces - AGONIZE miniconference

The celebrated Brill-Noether theorem says that the space of degree d maps of a general genus g curve to ℙr is irreducible. However, for special curves, this need not be the case. Indeed, for general k-gonal curves (degree k covers of ℙ1), this space of maps can have many components, of dif

From playlist Arithmetic Geometry is ONline In Zoom, Everyone (AGONIZE)

Genus of abstract modular curves with level ℓℓ structure - Ana Cadoret

Ana Cadoret Ecole Polytechnique; Member, School of Mathematics November 21, 2013 To any bounded family of 𝔽ℓFℓ-linear representations of the etale fundamental of a curve XX one can associate families of abstract modular curves which, in this setting, generalize the `usual' modular curves w

From playlist Mathematics

The congruence subgroup property for SL(2,Z) - William Yun Chen

Arithmetic Groups Topic: The congruence subgroup property for SL(2,Z) Speaker: William Yun Chen Affiliation: Member, School of Mathematics Date: November 10, 2021 Somehow, despite the title, SL(2,Z) is the poster child for arithmetic groups not satisfying the congruence subgroup property

From playlist Mathematics

Filip Najman, Q-curves over odd degree fields and sporadic points

VaNTAGe seminar June 29, 2021 License: CC-BY-NC-SA

From playlist Modular curves and Galois representations

Paola Frediani: Totally geodesic submanifolds in the Torelli locus

We will describe recent results on totally geodesic submanifolds and Shimura subvarieties of Ag contained in the Torelli locus Tg. Using the second fundamental form of the Torelli map we give an upper bound on the dimension of totally geodesic submanifolds contained in Tg, which depends on

From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"

Moduli of degree 4 K3 surfaces revisited - Radu Laza

Radu Laza Stony Brook University; von Neumann Fellow, School of Mathematics February 3, 2015 For low degree K3 surfaces there are several way of constructing and compactifying the moduli space (via period maps, via GIT, or via KSBA). In the case of degree 2 K3 surface, the relationship be

From playlist Mathematics

Algebraic geometry 44: Survey of curves

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.

From playlist Algebraic geometry I: Varieties

What is... an elliptic curve?

In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were

From playlist An Introduction to the Arithmetic of Elliptic Curves

The differential calculus for curves (II) | Differential Geometry 8 | NJ Wildberger

In this video we extend Lagrange's approach to the differential calculus to the case of algebraic curves. This means we can study tangent lines, tangent conics and so on to a general curve of the form p(x,y)=0; this includes the situation y=f(x) as a special case. It also allows us to deal

From playlist Differential Geometry

Elliptic Curves - Lecture 6a - Ramification (continued)

This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/

From playlist An Introduction to the Arithmetic of Elliptic Curves

Thoughts about Andrew Ogg’s (Torsion) conjecture - Barry C. Mazur

Celebration In Honor of the Frank C. and Florence S. Ogg Professorship Topic: Thoughts about Andrew Ogg’s (Torsion) conjecture Speaker: Barry C. Mazur Affiliation: Gerhard Gade University Professor, Harvard University Date: October 13, 2022 Ogg’s celebrated conjecture can be paraphrased

From playlist Mathematics