| Springer数学研究生教材系列之一 |
| 《曲线模英文(影印版)》 preface 1 parameter spaces: constructions and examples a parameters and moduli b construction of the hfibert scheme c tangent space to the hilbert scheme d extrinsic pathologies mumford's example other examples e dimension of the hilbert scheme f severi varieties g hurwitz schemes basic facts about moduli spaces of curves a why do fine moduli spaces of curves not exist? b moduli spaces we'll be concerned with c constructions of mg the teichmiiller approach the hodge theory approach the geometric invariant theory (g.i,t.) approach d geometric and topological properties .basic properties local properties complete subvarieties of mg cohomology of mg: hater's theorems cohomology of the universal curve cohomology of hfibert schemes structure of the tautological ring witten's conjectures and kontsevich's theorem e moduli spaces of stable maps techniques a basic facts about nodal and stable curves dualizing sheaves automorphisms b deformation theory overview deformations of smooth curves variations on the basic deformation theory plan universal deformations of stable curves deformations of maps c stable reduction results examples d interlude: calculations on the moduli stack divisor classes on the moduli stack existence of tautological families e grothendieck-riemann-roch and porteous grothendieck-riemann-roch chern classes of the hodge bundle chern class of the tangent bundle porteous' formula the hyperelliptic locus in m3 relations amongst standard cohomology classes divisor classes on hilbert schemes f test curves: the hyperelliptic locus in m3 begun g admissible covers h the hyperelliptic locus in m3 completed 4 construction of m3 a background on geometric invariant theory the g.i.t. strategy finite generation of and separation by invariants the numerical criterion stability of plane curves b stability of hilbert points of smooth curves the numerical criterion for hilbert points gieseker's criterion stability of smooth curves c construction of mg via the potential stability theorem the plan of the construction and a few corollaries the potential stability theorem limit linear series and brill-noether theory a introductory remarks on degenerations b limits of line bundles c limits of linear series: motivation and examples d limit linear series: definitions and applications limit linear series smoothing limit linear series limits of canonical series and weierstrass points limit linear series on flag curves inequalities on vanishing sequences the case p= 0 proof of the gieseker-petri theorem geometry of moduli spaces: selected results a irreducibility of the moduli space of curves b diaz' theorem the idea: stratifying the moduli space the proof c moduli of hyperelliptic curves fiddling around the calculation for an (almost) arbitrary family the picard group of the hyperelliptic locus d ample divisors on mg an inequality for generically hilbert stable families proof of the theorem an inequality for families of pointed curves ample divisors on mg e irreducibility of the severi varieties initial reductions analyzing a degeneration an example completing the argument f kodaira dimension of mg writing down general curves basic ideas pulling back the divisors dr divisors on mg that miss j(m2,1 \ w) divisors on mg that miss i(m0,g) further divisor class calculations curves defined over q bibliography index |
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