On SUSY curves
英文摘要：
In this note we give a summary of some elementary results in the theory of super Riemann surfaces (SUSY curves).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Moduli spaces of SUSY curves and their operads
This article generalizes the operad of moduli spaces of curves to SUSY curves. SUSY curves are algebraic curves with additional supersymmetric or supergeometric structure. Here, we focus on the description of the relevant category of graphs and its combinatorics as well as the construction of dual graphs of SUSY curves and the SUSY operad taking values in a category of moduli spaces of SUSY curves with Neveu-Schwarz and Ramond punctures.
math-phmath.AGmath.MP
The supermoduli of SUSY curves with Ramond punctures
We construct local and global moduli spaces of supersymmetric curves with Ramond-Ramond punctures. We assume that the underlying ordinary algebraic curves have a level n structure and build these supermoduli spaces as algebraic superspaces, i.e., quotients of étale equivalence relations between superschemes.
hep-thmath-phmath.AG
Moduli of log twisted $\mathcal{N} =1$ SUSY curves
The goal of the present paper is to construct a smooth compactification of the moduli superstack classifying pointed $\mathcal{N} =1$ SUSY (= $\text{SUSY}_1$) curves. This construction is based on the Abramovich-Jarvis-Chiodo compactification of the moduli stack classifying spin curves. First, we give a general framework of a theory of log superschemes (or more generally, log superstacks). Then, we introduce the notion of a pointed (stable) log twisted $\text{SUSY}_1$ curve; it may be thought of as a logarithmic and twisted generalization of the classical notion of a pointed $\text{SUSY}_1$ cu…
math.AG
Pluri-Canonical Models of Supersymmetric Curves
This paper is about pluri-canonical models of supersymmetric (susy) curves. Susy curves are generalisations of Riemann surfaces in the realm of super geometry. Their moduli space is a key object in supersymmetric string theory. We study the pluri-canonical models of a susy curve, and we make some considerations about Hilbert schemes and moduli spaces of susy curves.
hep-thmath.AG
带Ramond穿孔的零亏格SUSY曲线的超模空间
The supermoduli space of genus zero SUSY curves with Ramond punctures
该研究构造了带Ramond穿孔的零亏格超黎曼曲面超模空间及无SUSY结构的零亏格超曲线模空间的显式商，分别证明二者是Deligne-Mumford超栈与代数超栈。
hep-thmath.AGmath.QA
Teaching algebraic curves for gifted learners at age 11 by using LEGO linkages and GeoGebra
A summary of an experimental course on algebraic curves is given that was held for young learners at age 11. The course was a part of Epsilon camp, a program designed for very gifted students who have already demonstrated high interest in studying mathematics. Prerequisites for the course were mastery of Algebra I and at least one preliminary year in a prior Epsilon camp. The summary gives an overview of the flow of teaching, the achieved results and some evaluation of the given feedback.
math.AGmath.HO
更多相关论文收起更多论文
Descendent integrals and tautological rings of moduli spaces of curves
The main objective of this paper is to give a summary of our recent work on recursion formulae for intersection numbers on moduli spaces of curves and their applications. We also present a conjectural relation between tautological rings and the mock theta function.
math-phmath.AGmath.MP
Geometry of moduli spaces of meromorphic connections on curves, Stokes data, wild nonabelian Hodge theory, hyperkahler manifolds, isomonodromic deformations, Painleve equations, and relations to Lie theory
Summary of main work 1999-2012
math.AGmath.DGmath.HO
On algorithms to obtain linear determinantal representations of smooth plane curves of higher degree
We give two algorithms to compute linear determinantal representations of smooth plane curves of any degree over any field. As particular examples, we explicitly give representatives of all equivalence classes of linear determinantal representations of two special quartics over the field $\mathbb{Q}$ of rational numbers, the Klein quartic and the Fermat quartic. This paper is a summary of third author's talk at the JSIAM JANT workshop on algorithmic number theory in March 2018. Details will appear elsewhere.
math.AGmath.NT
On the Existence of Heterotic-String and Type-II-Superstring Field Theory Vertices
We consider two problems associated to the space of Riemann surfaces that are closely related to string theory. We first consider the problem of existence of heterotic-string and type-II-superstring field theory vertices in the product of spaces of bordered surfaces parameterizing left- and right-moving sectors of these theories. It turns out that this problem can be solved by proving the existence of a solution to the BV quantum master equation in moduli spaces of bordered spin-Riemann surfaces. We first prove that for arbitrary genus $g$, $n_{\text{NS}}$ Neveu-Schwarz boundary components, an…
hep-thmath-phmath.AG
Elliptic Fibrations and Elliptic Models
We study the Seiberg-Witten curves for N=2 SUSY gauge theories arising from type IIA string configurations with two orientifold sixplanes. Such theories lift to elliptic models in M-theory. We express the M-theory background for these models as a nontrivial elliptic fibration over C. We discuss singularities of this surface, and write the Seiberg-Witten curve for several theories as a subvariety of this surface.
hep-thmath.AG
Three lectures on elliptic surfaces and curves of high rank
Over the past two years we have improved several of the (Mordell-Weil) rank records for elliptic curves over Q and nonconstant elliptic curves over Q(t). For example, we found the first example of a curve E/Q with 28 independent points P_i in E(Q) (the previous record was 24, by R.Martin and W.McMillen 2000), and the first example of a curve over Q with Mordell-Weil group isomorphic with (Z/2Z) x Z^18 (the previous rank record for a curve with a 2-torsion point was 15, by Dujella 2002). In these lectures we give some of the background, theory, and computational tools that led to these new reco…
math.AGmath.NT
Group Compactifications and Moduli Spaces
We give a summary of joint work with Michael Thaddeus that realizes toroidal compactifcations of split reductive groups as moduli spaces of framed bundles on chains of rational curves. We include an extension of this work that covers Artin stacks with good moduli spaces. We discuss, for complex groups, the symplectic counterpart of these compactifications, and conclude with some open problems about the moduli problem concerned.
math.AG
