000			02219nam a22003135i 4500
001			90579
005			20240111190126.0
010			_a978-3-030-67829-6 _dcompra
090			_a90579
100			_a20231023d2021 k||y0pory50 ba
101	0		_aeng
102			_aCH
200	1		_aGeometric invariant theory, holomorphic vector bundles and the harder-narasimhan filtration _bDocumento eletrónico _fby Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas
210			_aCham _cSpringer International Publishing _cSpringer _d2021
215			_aXIII, 127 p. _cil.
225	2		_aSpringerBriefs in Mathematics
303			_aThis book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin's theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.
606			_aGeometria algébrica
606			_aTeoria dos módulos
606			_aInvariantes
680			_aQA564
700	1		_aZamora Saiz _bAlfonso
701	1		_aZúñiga-Rojas _bRonald A.
801		0	_aPT _gRPC
856	4		_uhttps://doi.org/10.1007/978-3-030-67829-6
942			_2lcc _cF _n0