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• https://drive.usercontent.google.com/download?id=1kXVklz1lRlQxUGNOye3Ff_ZdU9kNQzMe&export=download&authuser=0 — found via User

• https://mathoverflow.net/q/7988 — found via Mwmbl

  Riemann surfaces: explicit algebraic equations - MathOverflow

  Suppose $\Gamma$ is a nice discrete subgroup of $SL(2,\mathbb{R})$ such that the genus of the Riemann surface $\mathbb{H}/\Gamma$ is larger than 1. We kno…

  moduli spaces - Which Riemann surfaces arise from the Riemann ex… The following was already known to Riemann. Suppose that one is given a connected Riemann surface $X$, a finite set $\Delta \subset X$ and a homomorphism…
  big list - Reference in Riemann Surfaces - MathOverflow It depends partly what you are more interested in, geometry or analysis. There are two relevant categories: compact complex manifolds of dimension one (an…
  riemannian geometry - Systole of Riemann surfaces of genus $g$ -… In Buser and Sarnak's " On the period matrix of a Riemann surface of large genus ", we get $$\frac4{3}\le\limsup_{g\rightarrow\infty}\frac{\max\{\operator…
  riemann surfaces - Dessins d'enfant of Dynkin diagrams? - MathOv…
  riemann surfaces - Square root of the determinant line - MathOve… $\begingroup$I'm not sure what you mean by 'canonical'. For example, when $\Sigma$ has genus $1$, there are 4 distinct spin structures, one representing …
  riemann surfaces - Motivation behind defining the Ramification D… I would like to understand what exactly is the motivation for defining the notion of a ramification divisor of a function. As I see the definition, If $f…

• https://en.wikipedia.org/wiki/Riemann–Roch_theorem — found via Wikipedia

  Riemann–Roch theorem

  Initially proved as Riemann's inequality by Riemann (1857), the theorem reached its definitive form for Riemann surfaces after work of Riemann's short-lived student

  Riemann surface Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces
  Bernhard Riemann the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking

• https://math.stackexchange.com/a/46790 — found via Mwmbl

  riemann surfaces - Calculating monodromy - Mathematics Stack Exc…

  I'm right now learning about Monodromy from self-studying Rick Miranda's fantastic book "Algebraic Curves and Riemann surfaces". Today, I read about mono…

  riemann surfaces - The genus of the Fermat curve $x^d+y^d+z^d=0$… I need to calculate the genus of the Fermat Curve, and I'd like to be reviewed on what I have done so far; I'm not secure of my argumentation. Such curve…

• https://arxiv.org/abs/1602.08219 — found via Mwmbl

  [1602.08219] Algebraic deRham cohomology of log-Riemann surfaces…

  Abstract:Log-Riemann surfaces of finite type are Riemann surfaces with finitely generated fundamental group equipped with a local diffeomorphism to C suc…

  [1305.0469] CFTs on Riemann Surfaces of genus $g\geq 1$: Depende… Abstract:The dependence of the Virasoro-$N$-point function on the moduli of the Riemann surface is investigated. We propose an algebraic geometric approa…
  [1002.1676] Deformations of bordered Riemann surfaces and associ… Abstract: We consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, par…
  [1107.0102] Acyclic embeddings of open Riemann surfaces into new… Title:Acyclic embeddings of open Riemann surfaces into new examples of elliptic manifolds Abstract:The geometric notion of ellipticity for complex manifo…
  [1104.5471] Tensor models and embedded Riemann surfaces Title:Tensor models and embedded Riemann surfaces Abstract:Tensor models and, more generally, group field theories are candidates for higher-dimensional …
  [0710.3357] Riemann surfaces and AF-algebras Title:Riemann surfaces and AF-algebras Abstract:For a generic set in the Teichmueller space, we construct a covariant functor with the range in a categor…
  [1305.0469v4] CFTs on Riemann Surfaces of genus $g\geq 1$: Depen… Abstract:The dependence of the Virasoro-$N$-point function on the moduli of the Riemann surface is investigated. We propose an algebraic geometric approa…
  [1305.0469v2] CFTs on Riemann Surfaces of genus $g\geq 1$: Depen… Abstract:The dependence of the Virasoro-$N$-point function on the moduli of the Riemann surface is investigated. We propose an algebraic geometric approa…
  [1305.0469v3] CFTs on Riemann Surfaces of genus $g\geq 1$: Depen… Abstract:The dependence of the Virasoro-$N$-point function on the moduli of the Riemann surface is investigated. We propose an algebraic geometric approa…
  [1512.04035] On tube-log Riemann surfaces and primitives of rati… Abstract:For a generic class of rational functions, we give an explicit description of the flat structure on the Riemann sphere induced by a meromorphic …
  [1511.00652] Discrete Riemann surfaces based on quadrilateral ce… Abstract:Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces tog…
  [1305.0469v1] CFTs on Riemann Surfaces of genus $ g\geq 1$: Depe… Abstract:The dependence of the Virasoro-$N$-point function on the moduli of the Riemann surface is investigated. We propose an algebraic geometric approa…
  [math/0202156] Riemann Surfaces and 3-Regular Graphs Title:Riemann Surfaces and 3-Regular Graphs Abstract: In this thesis we consider a way to construct a rich family of compact Riemann Surfaces in a combin…
  [1209.2459v4] Notes On Super Riemann Surfaces And Their Moduli Abstract: These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understa…
  [0710.2326] The resultant on compact Riemann surfaces Title:The resultant on compact Riemann surfaces Abstract: We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface an…
  [1705.07627] Rational CFTs on Riemann surfaces Title:Rational CFTs on Riemann surfaces Abstract:The partition function of rational conformal field theories (CFTs) on Riemann surfaces is expected to sa…
  [2309.14522] Dimers on Riemann surfaces and compactified free fi… Title:Dimers on Riemann surfaces and compactified free field Abstract:We consider the dimer model on a bipartite graph embedded into a locally flat Riema…
  [1511.05001] Super Riemann Surfaces and the Super Conformal Acti… Abstract:Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmo…
  [1011.1632v2] CFTs on Riemann Surfaces of genus $g\geq 1$ Title:CFTs on Riemann Surfaces of genus $g\geq 1$ Abstract:N-point functions of holomorphic fields in rational conformal field theories can be calculated…
  [1209.2459] Notes On Super Riemann Surfaces And Their Moduli Title:Notes On Super Riemann Surfaces And Their Moduli Abstract:These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming t…
  [0909.3600v1] Discrete Riemann Surfaces and the Ising model Title:Discrete Riemann Surfaces and the Ising model Abstract: We define a new theory of discrete Riemann surfaces and present its basic results. The key …
  [1011.1632v5] CFTs on Riemann Surfaces of genus $g\geq 1$ Title:CFTs on Riemann Surfaces of genus $g\geq 1$ Abstract:$N$-point functions of holomorphic fields in conformal field theories can be calculated by met…
  [1011.1632v3] CFTs on Riemann Surfaces of genus $g\geq 1$ Title:CFTs on Riemann Surfaces of genus $g\geq 1$ Abstract:$N$-point functions of holomorphic fields in rational conformal field theories can be calculat…
  [1011.1632] CFTs on Riemann Surfaces of genus $g\geq 1$ Title:CFTs on Riemann Surfaces of genus $g\geq 1$ Abstract:$N$-point functions of holomorphic fields in conformal field theories can be calculated by met…
  [0911.0214] Orbifold Riemann surfaces and geodesic algebras Title:Orbifold Riemann surfaces and geodesic algebras Abstract: We study the Teichmüller theory of Riemann surfaces with orbifold points of order two usi…
  [0909.3600] Discrete Riemann Surfaces and the Ising model Title:Discrete Riemann Surfaces and the Ising model Abstract: We define a new theory of discrete Riemann surfaces and present its basic results. The key …
  [1709.02496] E-String Theory on Riemann Surfaces Title:E-String Theory on Riemann Surfaces Abstract:We study compactifications of the 6d E-string theory, the theory of a small E_8 instanton, to four dim…
  [1011.1632v4] CFTs on Riemann Surfaces of genus $g\geq 1$ Title:CFTs on Riemann Surfaces of genus $g\geq 1$ Abstract:$N$-point functions of holomorphic fields in conformal field theories can be calculated by met…
  [1011.1632v1] CFTs on Riemann Surfaces of genus $g\geq 1$ Title:CFTs on Riemann Surfaces of genus $g\geq 1$ Abstract:n-point functions of holomorphic fields in rational conformal field theories can be calculated…
  [1910.06221] Immersions of open Riemann surfaces into the Rieman… Title:Immersions of open Riemann surfaces into the Riemann sphere Abstract:In this paper we show that the space of holomorphic immersions from any given …
  [1209.2459v3] Notes On Super Riemann Surfaces And Their Moduli Title:Notes On Super Riemann Surfaces And Their Moduli Abstract:These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming t…
  [1209.2459v2] Notes On Super Riemann Surfaces And Their Moduli Title:Notes On Super Riemann Surfaces And Their Moduli Abstract:These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming t…
  [1209.2459v5] Notes On Super Riemann Surfaces And Their Moduli Title:Notes On Super Riemann Surfaces And Their Moduli Abstract:These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming t…
  [1106.3092] Degenerating Riemann surfaces and the Quillen metric Title:Degenerating Riemann surfaces and the Quillen metric Abstract:The degeneration of the Quillen metric for a one-parameter family of Riemann surfaces…
  [1209.2459v1] Notes On Super Riemann Surfaces And Their Moduli Title:Notes On Super Riemann Surfaces And Their Moduli Abstract:These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming t…
  [2407.06332] On affine Riemann surfaces Title:On affine Riemann surfaces Abstract:We show that the universal covering space of a connected component of a regular level set of a smooth complex v…
  [2309.14522v2] Dimers on Riemann surfaces and compactified free … Title:Dimers on Riemann surfaces and compactified free field Abstract:We consider the dimer model on a bipartite graph embedded into a locally flat Riema…
  [2309.14522v1] Dimers on Riemann surfaces and compactified free … Title:Dimers on Riemann surfaces and compactified free field Abstract:We consider the dimer model on a bipartite graph embedded into a locally flat Riema…
  [2101.09557] Padé\ approximants on Riemann surfaces and KP tau f… Title:Padé\ approximants on Riemann surfaces and KP tau functions Abstract:The paper has two relatively distinct but connected goals; the first is to def…
  [1910.06221v3] Immersions of open Riemann surfaces into the Riem… Title:Immersions of open Riemann surfaces into the Riemann sphere Abstract:In this paper we show that the space of holomorphic immersions from any given …
  [1309.7202] Poisson varieties from Riemann surfaces Title:Poisson varieties from Riemann surfaces Abstract:Short survey based on talk at the Poisson 2012 conference. The main aim is to describe and give so…
  [1711.08186] The Anomaly flow over Riemann surfaces Title:The Anomaly flow over Riemann surfaces Abstract:We initiate the study of a new nonlinear parabolic equation on a Riemann surface. The evolution equ…
  [1910.06221v1] Immersions of open Riemann surfaces into the Riem… Title:Immersions of open Riemann surfaces into the Riemann sphere Abstract:In this paper we establish the weak homotopy type of the space of holomorphic …
  [1709.02496v1] E-String Theory on Riemann Surfaces Title:E-String Theory on Riemann Surfaces Abstract:We study compactifications of the 6d E-string theory, the theory of a small E_8 instanton, to four dim…

• https://terrytao.wordpress.com/tag/riemann-surfaces/ — found via Mwmbl

  Riemann surfaces | What's new

  Previous set of notes: 246B Notes 4. Next set of notes: Notes 2. The fundamental object of study in real differential geometry are the real manifolds: Ha…