000			02124nam a22002777a 4500
003			IIITD
005			20250521173009.0
008			250514b |||||||| |||| 00| 0 eng d
020			_a9783031241536
040			_aIIITD
082			_a516.35 _bBUS-A
100			_aBuse, Laurent
245			_aAlgebraic curves and surfaces : _ba history of shapes _cby Laurent Buse, Fabrizio Catanese and Elisa Postinghel
260			_aSwitzerland : _bSpringer, _c©2023
300			_axiv, 205 p. : _bill. ; _c24 cm.
490			_aSISSA Springer Series _v4
505			_t1. The P12-Theorem: The Classification of Surfaces and Its Historical Development
505			_t2. Linear Systems of Hypersurfaces with Singularities and Beyond
505			_t3. Implicit Representations of Rational Curves and Surfaces
520			_aThis volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces and the classification theorem of algebraic surfaces by Castelnuovo and Enriques; the use of such a classical geometric approach, as the one introduced by Castelnuovo, to study linear systems of hypersurfaces; and the algebraic methods used to find implicit equations of parametrized algebraic curves and surfaces, ranging from classical elimination theory to more modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Since our subject has a long and venerable history, this book cannot cover all the details of this broad topic, theory and applications, but it is meant to serve as a guide for both young mathematicians to approach the subject from a classical and yet computational perspective, and for experienced researchers as a valuable source for recent applications. Collapse summary
650			_aAlgebraic Geometry
650			_aAlgebra
700			_aCatanese, Fabrizio
700			_aPostinghel, Elisa
942			_cBK _2ddc
999			_c189948 _d189948