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

• http://mathoverflow.net/a/77282 — found via Mwmbl

  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…

  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 - Dessins d'enfant of Dynkin diagrams? - MathOv…
  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…

• http://arxiv.org/abs/0710.3357 — found via Mwmbl

  [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…

  [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…
  [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…
  [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…
  [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…
  [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 …
  [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…
  [2309.14522] 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…
  [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…
  [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…
  [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…
  [1011.1632v5] 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…
  [1011.1632v2] 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 …
  [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…
  [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…
  [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…
  [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…
  [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…
  [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…
  [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…
  [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 …
  [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…
  [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…
  [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…
  [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…
  [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…
  [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…
  [1305.0469v4] 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…
  [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…
  [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 …
  [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…
  [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…
  [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 …
  [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…
  [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 …
  [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…
  [1102.3006] Unipotent Schottky bundles on Riemann surfaces and c… Title:Unipotent Schottky bundles on Riemann surfaces and complex tori Abstract:We study a natural map from representations of a free (resp. free abelian)…
  [1509.07044] Colliding holes in Riemann surfaces and quantum clu… Abstract:In this paper, we describe a new type of surgery for non-compact Riemann surfaces that naturally appear when colliding two holes or two sides of…
  [math/0010022] The moduli space of Riemann surfaces is Kahler hy… Title:The moduli space of Riemann surfaces is Kahler hyperbolic Abstract: Let $\cM_{g,n}$ be the moduli space of Riemann surfaces of genus $g$ with $n$ p…
  [1805.06405] Lectures notes on compact Riemann surfaces Title:Lectures notes on compact Riemann surfaces Abstract:This is an introduction to the geometry of compact Riemann surfaces, largely following the book…

• 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://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…