moduli stack of Gieseker-SL2-bundles on a Nodal curve II

by Takeshi Abe

Publisher: Kyōto Daigaku Sūri Kaiseki Kenkyūjo in Kyoto, Japan

Written in English
Published: Pages: 15 Downloads: 221
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References. The original articles are: Ofer Aharony, Amihay Hanany, Branes, Superpotentials and Superconformal Fixed Points, Nucl. Phys. B, (arXiv:hep-th/). Ofer Aharony, Amihay Hanany, Barak Kol, Webs of (p, q) (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams, JHEP , (arXiv:hep-th/). Oren Bergman, Gabi Zafrir, Lifting 4d . While our paper was circulating, we were told in by Maxim Kontsevich that he had also discovered the stack of twisted stable maps, but had not written down the theory. His mo.   Let be the stack parameterizing pairs (S,C) such that (S,L) is a smooth primitively polarized K3 surface of genus g and C∈|L| is a stable curve. One can consider the obvious projection ⁠, where is the moduli stack of stable curves of genus g. Let be the image of c g restricted to pairs (S,C) such that C is smooth. This dissertation studies stability of 3-dimensional quadratic AS-regular algebras and their moduli. A quadratic algebra defined by a regular triple (E, L, σ) is stable if there is no node or line component of E fixed by σ. We first prove stability of the twisted homogeneous coordinate ring B(E, L, σ), then lift stability to that of A(E, L, σ) by analyzing the central element c₃ where B.

The moduli stack classifies families of smooth projective curves of genus, together with their isomorphisms. When g > 1, this stack may be compactified by adding new "boundary" points which correspond to stable nodal curves (together with their isomorphisms). A curve is stable if it has only a finite group of automorphisms. " Low Profile Stainless Steel Geissele Super Gas Block Included The Super Modular Rail (SMR) MK8 M-LOK™ is Geissele’s ultra-modular model. The SMR MK8 is one of the first rails available to utilize the Magpul M-LOK technology. These r. Through-Thickness Reinforcement (TTR) technologies are well suited to improving the mechanical properties in the out-of-plane direction of fibre-reinforced composites. However, besides the enhancement of delamination resistance and thus the prevention of overall catastrophic failure, the presence of additional reinforcement elements in the composite structure affects also the mechanical.   1 Introduction Hurwitz loci have played a basic role in the study of the moduli space of curves at least since when Clebsch, and later Hurwitz, proved that [g] is irreducible by showing that a certain Hurwitz space parameterizing coverings of [1] is connected (see [Hu], or [Fu2] for a modern proof).

Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack . The Hodge bundle on the moduli space of curves (of fixed genus) is roughly a vector bundle whose fiber over a curve C is the vector space. hyperelliptic A curve is hyperelliptic if it has a g 1 2 (i.e., there is a linear system of dimension 1 and degree 2.) hyperplane bundle Another term for Serre's twisting sheaf.

moduli stack of Gieseker-SL2-bundles on a Nodal curve II by Takeshi Abe Download PDF EPUB FB2

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Let X0 be an irreducible projective nodal curve with only one singular point, and let P0 be a line bundle on X0. The moduli SUX0(r; P0) of rank r vector bundles on X0 with determinant P0 is not compact.

In [A], using the technique of Kausz ([K1], [K2]), we constructed a compactification GSL2B(X0; P0) of SUX0(2; P0). THE MODULI STACK OF GIESEKER-SL2-BUNDLES ON A NODAL CURVE bundles with fixed determinant on a nodal curve, and show that their moduli stack is normal crossing.

of the moduli Author: Ivan Kausz. The Moduli Stack of Rank-two Gieseker Bundles with Fixed Determinant on a Nodal Curve (T Abe) Vector Bundles on Curves and Theta Functions (A Beauville) On the Finiteness of Abelian Varieties with Bounded Modular Height (A Moriwaki) Moduli of Regular HolonomicD X-modules with Natural Parabolic Stability (N Nitsure).

One of the first is the dualizing sheaf of a nodal curve, which is the analogue of the canonical bundle of a smooth curve. The authors then describe, by taking a point as the base, the scheme-theoretic automorphism group of a stable curve, and show that it is finite and reduced. After a brief interlude on the properties of the moduli stack Cited by: moduli space is that the moduli space not really a space but a stack.

As a result, to Deligne-Mumford stacks from the perspective of the moduli space of curves. The book by Laumon and Moret-Bailly [LMB] is the most comprehensive (and De nition (Stable curves) A curve Cof arithmetic genus g 2 is stable if it is connected, has at.

These notes touch on all four aspects of the study of moduli spaces of curves – complex analytic, topological, algebro-geometric, and number theoretic. Contents 1. Introduction to Elliptic Curves and the Moduli Problem 3 2. Families of Elliptic Curves and the Universal Curve 11 3. The Orbifold M1,1 17 4.

The Orbifold M1,1 and Modular Forms 29 5. S2 Network Node VR is an efficient way to deliver access control and video management in a distributed environment. Each S2 Network Node VR supports up to eight IP cameras and up to eight portals and houses up to four S2 application blades for access control, inputs, outputs and temperature probes.

MODULI OF NODAL CURVES ON K3 SURFACES C. CILIBERTO, F. FLAMINI, C. GALATI, AND A. KNUTSEN Abstract. We consider modular properties of nodal curves on general K3surfaces.

Let Kp be the moduli space of primitively polarized K3 surfaces (S,L) of genus p> 3 and Vp,m,δ → Kp be the. Macaulay stack has a dualizing sheaf and it is an invertible sheaf when it is Gorenstein. As an application of this general machinery we compute the dualizing sheaf of a tame nodal curve.

Contents Overview 1 Acknowledgements 2 1. Foundation of duality for stacks 3 History 3. As is explained in the book’s introduction, its focus shifted towards moduli as it evolved.

This must have had a lot to do with the appearance of D. Mumford’s paper [in Arithmetic and geometry, Vol. II, –, Progr. Math., 36, Birkhauser Boston, Boston, MA, ;¨ MR   The study of Severi varieties is classical and closely related to modular properties. For the case of nodal plane curves the traditional reference is Severi's wide exposition in [23, Anhang F], although already in Enriques–Chisini's famous book [9, vol.

III, chapt. III, §33] families of plane nodal curves with general moduli have been. disconnected) algebraic curve C~ along marked points.

Now we can go to the compacti cation: For 2g 2 + n>0 there is a smooth, proper Deligne-Mumford (ne) moduli stack Mg;n of stable, con-nected nodal curves of arithmetic genus gtogether with nlabeled markings, which are pairwise disjoint and also disjoint from the nodes.

Stability means. Math. (), ] for the moduli stack of G-bundles over a curve, and of analogous statements for the moduli stacks and spaces of bundles with parabolic structures. Hiro Tanaka "Morse theory and the stack of broken lines" Yi Xie "Ring structure of the cohomology of the moduli of bundles over a curve and instanton Floer homology" ref 1 2 Jie "The Tropical Vertex II" paper Yi Li "Lower Bounds for Nodal Sets of Eigenfunctions" paper 1 2 3: December 2.

The moduli stack classifies families of smooth projective curves of genus g, together with their isomorphisms. When g > 1, this stack may be compactified by adding new "boundary" points which correspond to stable nodal curves (together with their isomorphisms).

A curve is stable if it has only a finite group of automorphisms. M¯ g,n and M¯ g,n,d(M,J) We will describe a compactification M¯ g,n of Mg,n called the Deligne-Mumford moduli space. It is a stratified space.

The top stratum is Mg,n and the other strata are isomorphism classes [Σ,s∗,ν,j] of marked nodal Riemann surfaces (Σ,s∗,ν,j) of arith- metic genus g with n marked points s∗ as before.

There is a similar compactification M¯. Let (C,s 1,s n) be a nodal pointed curve of genus g, b 1,b n nonnegative rational numbers, and k a positive integer such that eachkb i is integral. Assume thatL≔ω C k (b 1 s 1 +⋯+b n s n) is nef and has positive degree.

For N⩾3 the sections of L N induce a dominant morphism r: C→C′ to a nodal curve of genus g. Notation for moduli spaces and boundary divisor classes Denote by M 0;0 the category whose objects are proper, at families ˇ: C!M of connected, at-worst-nodal, arithmetic genus 0 curves, and whose morphisms are Cartesian diagrams of such families.

This category is a smooth Artin stack over 3. Coherent systems on a nodal curve Usha N. Bhosle Brill-Noether bundles and coherent systems on special curves L. Brambila-Paz and Angela Ortega Higgs bundles in the vector representation N.

Hitchin Moduli spaces of torsion free sheaves on nodal curves C. Seshadri. (source: Nielsen Book Data). We consider the moduli of elliptic curves with G-structures, where G is a finite 2-generated group. When G is abelian, a G-structure is the same as a classical congruence level structure.

There is a natural action of $$\\text {SL}_2(\\mathbb {Z})$$ SL 2 (Z) on these level structures. If $$\\Gamma $$ Γ is a stabilizer of this action, then the quotient of the upper half plane by $$\\Gamma.

A major barrier to constructing these spaces is that, while the moduli space of fixed-degree line bundles on a nodal curve exists, it typically does not have nice properties: often it has infinitely many connected components (that is, is not of finite.

Stack Exchange network consists of Q&A communities including Stack Overflow, (now bundled together with the red book in LNM ) Lecture IV. In Lecture II (same place) Mumford sketches two more "coordinate oriented" methods.

Moduli problem of stable nodal curves over the integers. Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry.

In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory.

CONTRACTOR W. Aiport Bevard, Site Ht, Tex eg. Sig Lightig Goup. A Right Reeve TSC Proof of Caldararu's conjecture by D. Huybrechts and P.

Stellari On integral Hodge classes on uniruled or Calabi-Yau threefolds by C. Voisin Birational geometry of symplectic resolutions of nilpotent orbits by Y. Namikawa The moduli stack of rank-two Gieseker bundles with fixed determinant on a nodal curve by T. Abe Vector bundles on curves and. Moduli stacks of stable curves.

The moduli stack classifies families of smooth projective curves, together with their isomorphisms. When >, this stack may be compactified by adding new "boundary" points which correspond to stable nodal curves (together with their isomorphisms).A curve is stable if it is complete, connected, has no singularities other than double points, and has only a finite.

Theorem II, Theorem II], and it equals hc 1(T X); i+ dim(X) + r 3: Because E is perfect, via the det-div formalism of [5], there is an associated invert- ible sheaf det(E) on Mthat is locally isomorphic to det(F0) det(F 1) invertible sheaf is the virtual canonical bundle.

When M 0;r(X;) is integral and when the dimension equals the virtual dimension. By Brill-Noether theory, the generic genus $6$ curve is birational to a sextic plane curve in $\mathbb{P}^2$.

I was wondering if there is a direct/natural construction of this birational map. In ot. Abstract: For a stable curve of arithmetic genus and the determinant of cohomology line bundle on Bun, we show that the section ring for the pair is finitely generated.

Applications involving vector bundles of conformal blocks are given, including quasi polynomiality at.

$\begingroup$ I think that the huge book Geometry of algebraic curves II by Arbarello, Cornalba, and Griffiths could be useful. Also in Liu's Algebraic geometry and arithmetic curves there is a section devoted to stable curves.

$\endgroup$ – Andrea Jun 1 '12 at. Abstract. The following is an expanded version of my talk at the symposium to celebrate ri’s seventieth birthday. The aim of the talk was to summarise the work of C.S.

Seshadri on the Moduli spaces of vector bundles on singular curves.nodal curves with possible degenerate scalings as follows. Definition (a) (Dualizing sheaf and its projectivization).

Recall from e.g. [Arbarello et al.p. 91]that if C is a genus zero nodal curve then the dualizing sheaf! C on C is locally free of rank one, that is, a line bundle. Explic.Additional Sources for Math Book Reviews; About MAA Reviews; Mathematical Communication; Information for Libraries; Author Resources; Advertise with MAA; Meetings.

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