|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910484256703321 |
|
|
Autore |
Mochizuki Takuro <1972-> |
|
|
Titolo |
Donaldson type invariants for algebraic surfaces : transition of moduli stacks / / Takuro Mochizuki |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Berlin, : Springer, c2009 |
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[1st ed. 2009.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (XXIII, 383 p.) |
|
|
|
|
|
|
Collana |
|
Lecture notes in mathematics, , 0075-8434 ; ; 1972 |
|
|
|
|
|
|
Classificazione |
|
14D2014J6014J80 |
MAT 142f |
MAT 146f |
SI 850 |
|
|
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Surfaces, Algebraic |
Invariants |
Moduli theory |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
Bibliographic Level Mode of Issuance: Monograph |
|
|
|
|
|
|
Nota di bibliografia |
|
Includes bibliographical references (p. 341-345) and index. |
|
|
|
|
|
|
Nota di contenuto |
|
Preliminaries -- Parabolic L-Bradlow Pairs -- Geometric Invariant Theory and Enhanced Master Space -- Obstruction Theories of Moduli Stacks and Master Spaces -- Virtual Fundamental Classes -- Invariants. |
|
|
|
|
|
|
|
|
Sommario/riassunto |
|
We are defining and studying an algebra-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We are interested in relations among the invariants, which are natural generalizations of the "wall-crossing formula" and the "Witten conjecture" for classical Donaldson invariants. Our goal is to obtain a weaker version of these relations, by systematically using the intrinsic smoothness of moduli spaces. According to the recent excellent work of L. Goettsche, H. Nakajima and K. Yoshioka, the wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case! |
|
|
|
|
|
|
|