tailieunhanh - Đề tài "Non-quasi-projective moduli spaces "

We show that every smooth toric variety (and many other algebraic spaces as well) can be realized as a moduli space for smooth, projective, polarized varieties. Some of these are not quasi-projective. This contradicts a recent paper (Quasi-projectivity of moduli spaces of polarized varieties, Ann. of Math. 159 (2004) 597–639.). A polarized variety is a pair (X, H) consisting of a smooth projective variety X and a linear equivalence class of ample divisors H on X. For simplicity, we look at the case when X is smooth, numerical and linear equivalence coincide for divisors on X, H is very. | Annals of Mathematics Non-quasi-projective moduli spaces By J anos Koll ar Annals of Mathematics 164 2006 1077 1096 Non-quasi-projective moduli spaces By Janos Kollar Abstract We show that every smooth toric variety and many other algebraic spaces as well can be realized as a moduli space for smooth projective polarized varieties. Some of these are not quasi-projective. This contradicts a recent paper Quasi-projectivity of moduli spaces of polarized varieties Ann. of Math. 159 2004 597-639. . A polarized variety is a pair X H consisting of a smooth projective variety X and a linear equivalence class of ample divisors H on X. For simplicity we look at the case when X is smooth numerical and linear equivalence coincide for divisors on X H is very ample and H X Ox mH 0 for i m 0. A well established route to construct moduli spaces of such pairs is to embed X into Pw by H . The pair X H and the embedding X Pw determine each other up to the action of PGL N 1 . Deformations of X H cover an open subset U X H of the Hilbert scheme Hilb Pw with Hilbert polynomial x X Ox mH . One can then view the quotient U X H PGL N 1 as the moduli space of the pairs X H . See MF82 App. 5 or Vie95 Ch. 1 for general introductions to moduli problems. The action of PGL N 1 can be bad along some orbits and therefore one has to make additional assumptions to ensure that the quotient U X H PGL N 1 is reasonable. The optimal condition seems to be to require that the action be proper. This is equivalent to assuming that U X H PGL N 1 exists as a separated complex space or as a separated algebraic space Kol97 KM97 . A difficult result of Viehweg cf. Vie95 shows that if the canonical class Kx is assumed nef then U X H PGL N 1 is a quasi-projective scheme. A recent paper ST04 asserts the quasi-projectivity of moduli spaces of polarized varieties for arbitrary Kx whenever the quotient U X H PGL N 1 exists as a separated algebraic space. The aim of the present note is to confute this claim. The .

• Thạc sĩ - Tiến sĩ - Cao học
• Non quasi projective
• subjects of mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Research methods
• Data collection methods
• Understanding scientific research
• Ensuring research validity
• Measurement techniques
• Sampling methods
• Scientific research capacity
• Educational institutions
• Policy and management studies
• Vietnam Academy for Ethnic minorities
• Scientific bases
• earth sciences
• Research
• VNU Journal of Science
• scientific reports
• Action research
• linguistics
• research projects
• Foreign Languages
• cooperative research
• Renewable energy
• Introduction to research
• Scientific investigation
• Scientific investigation research
• Experimental designs
• Measurement of variables
• Reading research
• Conducting and reading research
• Research process
• Research report
• Purpose of research
• Scientific method
• Conducting research
• The effect of university autonomy on training and scientific research
• Vietnam national university of agriculture
• Training and scientific research
• Vascular plant
• Flora
• Yen Tu
• Quang Ninh Research Forest
• statements and documents scientific reports
• medical reports
• medical knowledge
• medical research
• clinical trials
• medical management
• health care
• Methods in behavioral research
• Behavioral research
• Scientific understanding
• Fundamental research issues
• Measurement concepts
• Observational methods
• reading comprehension
• education
• optimal picket
• model creation
• urban expansion
• organizing spatial
• Journal of Science
• Journal of Technology
• Technology Management
• Research quality
• Strategy and policy
• Summary of Doctoral thesis
• Summary of Doctoral thesis in public Management
• State management
• Female scientific research human
• Research human resource development
• Scientific research and teaching
• Defense and security education
• Current situation and solutions
• Security education
• Structural biochemistry
• epigenetics
• MicroRNAs
• Tạp chí khoa học
• Tạp chí Công nghệ
• Quản lý công nghệ
• Human resources
• Science management
• Poliomyelitis vaccine Research
• Non Ri Maprec
• Production center