000			01916nam a22002655i 4500
001			92366
005			20231110183351.0
010			_a978-3-030-75174-6 _dcompra
090			_a92366
100			_a20231023d2021 k||y0pory50 ba
101	0		_aeng
102			_aCH
200	1		_aHow many zeroes? _bDocumento eletrónico _ecounting solutions of systems of polynomials via toric geometry at infinity _fby Pinaki Mondal
210			_aCham _cSpringer International Publishing _d2021
215			_aXV, 352 p. _cil.
225	2		_aCMS/CAIMS books in mathematics _v2
303			_aThis graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field K. The text collects and synthesizes a number of works on Bernstein's theorem of counting solutions of generic systems, ultimately presenting the theorem, commentary, and extensions in a comprehensive and coherent manner. It begins with Bernstein's original theorem expressing solutions of generic systems in terms of the mixed volume of their Newton polytopes, including complete proofs of its recent extension to affine space and some applications to open problems. The text also applies the developed techniques to derive and generalize Kushnirenko's results on Milnor numbers of hypersurface singularities, which has served as a precursor to the development of toric geometry. Ultimately, the book aims to present material in an elementary format, developing all necessary algebraic geometry to provide a truly accessible overview suitable to a second-year graduate students.
606			_aAlgebraic geometry
680			_aQA564-609
700			_970570 _aMondal _bPinaki
801		0	_aPT _gRPC
856	4		_uhttps://doi.org/10.1007/978-3-030-75174-6
942			_2lcc _cF _n0