LEADER 05184nam 22006975 450 001 9910480199803321 005 20200629231836.0 010 $a1-4612-4264-9 024 7 $a10.1007/978-1-4612-4264-2 035 $a(CKB)3400000000090775 035 $a(DE-He213)978-1-4612-4264-2 035 $a(SSID)ssj0001297699 035 $a(PQKBManifestationID)11822205 035 $a(PQKBTitleCode)TC0001297699 035 $a(PQKBWorkID)11229013 035 $a(PQKB)10850740 035 $a(MiAaPQ)EBC3075672 035 $a(PPN)23806736X 035 $a(EXLCZ)993400000000090775 100 $a20121227d1995 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Moduli Space of Curves$b[electronic resource] /$fedited by Robert H. Dijkgraaf, Carel Faber, Gerard B.M. van der Geer 205 $a1st ed. 1995. 210 1$aBoston, MA :$cBirkhäuser Boston :$cImprint: Birkhäuser,$d1995. 215 $a1 online resource (XII, 563p.) 225 1 $aProgress in Mathematics,$x0743-1643 ;$v129 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-8176-3784-2 311 $a1-4612-8714-6 320 $aIncludes bibliographical references. 327 $aDistribution of rational points and Kodaira dimension of fiber products -- How many rational points can a curve have? -- Quantum cohomology of rational surfaces -- Quantum intersection rings -- Mirror symmetry and elliptic curves -- A generalized Jacobi theta function and quasimodular forms -- Boundary behaviour of Hurwitz schemes -- Operads and moduli spaces of genus 0 Riemann surfaces -- Resolution of diagonals and moduli spaces -- The Chow ring of the moduli space of curves of genus 5 -- The cohomology of algebras over moduli spaces -- Enumeration of rational curves via torus actions -- Cellular decompositions of compactified moduli spaces of pointed curves -- Generating functions in algebraic geometry and sums over trees -- Holomorphicity and non-holomorphicity in N = 2 supersymmetric field theories -- An arithmetic problem in surface geometry -- An orbifold partition of $$ \bar M_g^n $$ -- Moduli of curves with non-abelian level structure -- Q-structure of conformal field theory with gauge symmetries -- On the cohomology of moduli spaces of rank two vector bundles over curves. 330 $aThe moduli space Mg of curves of fixed genus g ? that is, the algebraic variety that parametrizes all curves of genus g ? is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory. Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science." Witteen?s conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory. 410 0$aProgress in Mathematics,$x0743-1643 ;$v129 606 $aAlgebra 606 $aTopology 606 $aAlgebraic topology 606 $aAlgebraic geometry 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aAlgebra. 615 0$aTopology. 615 0$aAlgebraic topology. 615 0$aAlgebraic geometry. 615 14$aAlgebra. 615 24$aTopology. 615 24$aAlgebraic Topology. 615 24$aAlgebraic Geometry. 676 $a514 702 $aDijkgraaf$b Robert H$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aFaber$b Carel$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aGeer$b Gerard B.M. van der$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910480199803321 996 $aThe Moduli Space of Curves$91922509 997 $aUNINA