Parametrization of the moduli space of hyperelliptic and symmetric riemann surfaces article pdf available in annales academiae scientiarum. The geometric moduli spaces are studied via maps into the period domains. Good geometry of the moduli spaces of riemann surfaces. How to print part of pdf file and remove empty white space. It is a thermal heat printer, swecoin zebra technogies ttp 2030. The international max planck research school on moduli spaces imprs is the graduate program of the max planck institute for mathematics in bonn mpim jointly offered with the university of bonn. F g, the isotopy classes of orientation preserving di. The page cuts off at the appropriate page on the bottom, but i am left with 3 of blank white space at the top. Moduli spaces london mathematical society lecture note. The corresponding functor is open and bounded matsusakas big theorem, hence there is an algebraic stack m, which is a delignemumford stack if the automorphism group of xis nite. Moduli spaces of sheaves of rank 2 on a surface are not smooth, unless we consider sheaves with special invariants on special surfaces. One of the multiple factors that led us to write this article is that the origin and history of teichmu. The moduli space of einstein metrics is then called the covariant phase space.
The moduli space of flat sl2,rconnections modulo gauge transformations on the torus may be described by ordered pairs of commuting sl2,r matrices. The same proof shows that there is a ne moduli space m 0. Curves of genus g, onedimensional subspaces of rn, finite sets. Create pdfs with integrated fully functional word, powerpoint, and excel addins. Let mg,k te the moduli space of riemann surfaces of genus g with k punctures. The method of parametrizing moduli spaces by subsets of hilbert schemes, yields a natural compactification, since hilbert schemes are projective, but since all isomorphism classes of the original type were already present before compactifying, it is unclear what geometric objects the new points added correspond to. International max planck research school on moduli spaces. Concerning the geometry of moduli spaces of sheaves of higher rank, there are two guiding principles for the investigation. Moduli theory is the study of how objects, typically in algebraic geometry but sometimes in other areas of mathematics, vary in families and is fundamental to an understanding of the objects themselves. It is part of the bonn international graduate school in mathematics bigsmathematics. In this paper, we investigate the apparent singularities and the dual parameters of rank 2 parabolic connections on p 1 and rank 2 parabolic higgs bundles on p 1. The moduli space of flat sl2,rconnections modulo gauge transformations on the torus may be described by ordered pairs of commuting sl2,r matrices modulo simultaneous conjugation by sl2,r.
An introduction to moduli spaces of curves and its. Moduli spaces from a topological viewpoint 387 map of the diff1f action, sctf tf locally has a section, so that. Streamline workflow by converting paper contracts, agreements, and other documents to electronic pdf files. A formal universal deformation is by definition a formal scheme over a complete local ring, with special fiber the scheme over a field being studied, and with a universal property amongst such. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. Mcmullen proved that the moduli spaces of riemann surfaces are k. The above illustration shows a variant woodcut printer s device on verso last leaf of rare xvi century edition of platos timaeus, divini platonis operum a marsilio ficino tralatorum, tomus quartus. When is differential geometry on moduli spaces possible and. Fundamental ofs teichmuller and moduli spaces we briefly recall the fundamental theory of the geometry of teichmiiller and moduli spaces of hyperbolic riemann surfaces in this section. References about moduli space of abelian varieties with. How to eliminate excessive white space on top of page when. Minicourse on moduli spaces emily clader june 2011 1 what is a moduli space. Create pdf files,create pdf documents foxit reader.
In the context of the theory of gravity, the moduli space of pseudoriemannian metrics on x x is the configuration space of the field theory of gravity general relativity. Moduli spaces can be thought of as giving a universal space of parameters for the problem. In the course of one of my research project, i have been advised to try to have a look to moduli space of abelian varieties with level structure. The total space and the base space both being contractible, they concluded that diff1fand hence any other connected component of difff is contractible. Our aim is to understand the topological nature of. N is a ne moduli space for the moduli problem of nite sets up to bijection. Why does acrobat x compress empty white space when printing. Most of the results can be found in 5, 6, 7 and 18. I have a pdf document with a header and footer, but the middle is blank.
Parametrization of the moduli space of hyperelliptic and symmetric riemann surfaces article pdf available in annales academiae scientiarum fennicae mathematica 221 january 1997 with 18 reads. The most basic problem is that of moduli of smooth complete curves of a fixed genus. That is, the points of a moduli space correspond to solutions of geometric problems. The key feature of the space rp1, considered as the moduli space of lines in the plane, is that it captures the ways in which lines can modulate, or vary continuously in families. Nevertheless, something is known about the type of singularities they can attain. Moduli spaces of hyperk ahler manifolds and mirror symmetry. The printer s device to the colophon shows a medaillon with a. Moreover, we hope to develop a better understanding of some tools or concepts used in algebraic topology and algebraic geometry to attack moduli problems. Moduli theory is the study of how objects, typically in algebraic geometry but sometimes in other areas of mathematics, vary in families and is fundamental to. Later expositions include wilsons bpsampler mentioned above and section 2 of hopkinsluries ambidexterity paper 4 a nice addition to the topic was the 1994 hopkinshunton paper on the structure of spaces representing a landweber exact cohomology theory. The main references for this course are the books of newstead 31 and mukai 24 on moduli problems and git, and the book of mumford 25 on git. One also distinguishes between fine and coarse moduli spaces for the same moduli problem.
Pdf parametrization of the moduli space of hyperelliptic. Moduli spaces we consider the moduli problem for fano complex manifolds, i. We introduce the moduli space of genus, pointed curves, with enough information. Pdf parametrization of the moduli space of flat sl2, r. A p 2, which act faithfully and transitively on the bres of m i. Printers spaces crossword clue answer crossword heaven.
Some notes containing a brief survey of the cohomology of the moduli space of curves and the harerzagier formula for the orbifold euler characteristic. However, it is known that some moduli spaces of algebrogeometric objects have severe pathologies ex. Create standard compliant pdfs that are compatible with other pdf products. Most of the talks are given by nonexperts that would like to learn more about the subject. Introductory school on moduli spaces max planck institute. In sections 3 and 4 we introduce these moduli spaces as well as the corresponding period domains. The author mentions the moduli space of triangles, up to similarity.
Its cohomology ring has a elegant structure, and mumford suggested studying the moduli space of curves in the same way. Compact moduli spaces of del pezzo surfaces and kahlereinstein metrics odaka, yuji, spotti, cristiano, and sun, song, journal of differential geometry, 2016 einstein spaces as attractors for the einstein flow andersson, lars and moncrief, vincent, journal of differential geometry, 2011. Compactified moduli spaces of rational curves in projective homogeneous varieties chung, kiryong, hong, jaehyun, and kiem, younghoon, journal of the mathematical society of japan, 2012. I am generating a pdf that appears perfect on the monitor, but when i print it, it has excessive white space at the top. The step to moduli spaces, properly speaking, is an algebraization question, and has been largely put on a firm basis by artins approximation theorem. Opaque this complete moduli for fibered surfaces dan abramovich. Minicourse on moduli spaces university of michigan. Nontrivial symmetries of equilateral triangles over the circle seems to be the rotation around the center of the triangle. By those two software, you can print pdf to a4 paper and remove empty white space easily. The geometry of the moduli space tells you things about the geometry of the spaces points in it.
People tend to say classifying space when in the context of topology, and they tend to say moduli space when in a context of complex geometry or algebraic geometry. Moduli spaces are spaces of solutions of geometric classification problems. The moduli space is a quotient of the contractible teichmul. Suppose that we want to classify some kind of object, for example. What is a good introductory text for moduli theory. Some of the main results about compact hyperk ahler. The aim of the school is to understand several examples of moduli spaces.
Princeton university library one washington road princeton, nj 085442098 usa 609 2581470. This is precisely what i read when i see the space of vacua for the quantum field theory is a manifold or orbifold, usually called the vacuum manifold. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Angelo vistoli 1 introduction all the schemes with which we work will be schemes over the.
Then we obtain explicit descriptions of zariskiopen sets of the moduli space of the parabolic connections and the moduli space of the higgs bundles. I added a few words outlining other work of harer on the stability of the cohomology of the moduli space of curves. Ingeometryoneusuallywantstodefineinvariantsof thespaces,orgeometricobjects,underconsideration. Why does acrobat x compress empty white space when printing pdf files. The study of moduli spaces is an old branch of algebraic geometry with an abundance of technical tools.680 609 811 289 1276 527 1533 1583 304 805 934 808 1258 1420 856 291 1504 267 118 963 76 442 438 336 580 1009 1322 1198 1458 1122 1044 1378 2