001440857 000__ 03858cam\a2200565\i\4500
001440857 001__ 1440857
001440857 003__ OCoLC
001440857 005__ 20230309004706.0
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001440857 008__ 211111s2021\\\\sz\a\\\\ob\\\\001\0\eng\d
001440857 019__ $$a1285122341$$a1285149563$$a1285164304$$a1285238694$$a1294368242
001440857 020__ $$a9783030751746$$q(electronic bk.)
001440857 020__ $$a3030751740$$q(electronic bk.)
001440857 020__ $$z9783030751739$$q(print)
001440857 020__ $$z3030751732
001440857 0247_ $$a10.1007/978-3-030-75174-6$$2doi
001440857 035__ $$aSP(OCoLC)1285074609
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001440857 049__ $$aISEA
001440857 050_4 $$aQA564
001440857 08204 $$a516.3/5$$223
001440857 1001_ $$aMondal, Pinaki,$$eauthor.
001440857 24510 $$aHow many zeroes? :$$bcounting solutions of systems of polynomials via toric geometry at infinity /$$cPinaki Mondal.
001440857 264_1 $$aCham, Switzerland :$$bSpringer,$$c2021.
001440857 300__ $$a1 online resource (xv, 352 pages) :$$billustrations (some color)
001440857 336__ $$atext$$btxt$$2rdacontent
001440857 337__ $$acomputer$$bc$$2rdamedia
001440857 338__ $$aonline resource$$bcr$$2rdacarrier
001440857 347__ $$atext file
001440857 347__ $$bPDF
001440857 4901_ $$aCMS/CAIMS books in mathematics,$$x2730-6518 ;$$vvolume 2
001440857 504__ $$aIncludes bibliographical references and index.
001440857 5050_ $$aIntroduction -- A brief history of points of infinity in geometry -- Quasiprojective varieties over algebraically closed fields -- Intersection multiplicity -- Convex polyhedra -- Toric varieties over algebraically closed fields -- Number of solutions on the torus: BKK bound -- Number of zeroes on the affine space I: (Weighted) Bézout theorems -- Intersection multiplicity at the origin -- Number of zeroes on the affine space II: the general case -- Minor number of a hypersurface at the origin -- Beyond this book -- Miscellaneous commutative algebra -- Some results related to schemes -- Notation -- Bibliography.
001440857 506__ $$aAccess limited to authorized users.
001440857 520__ $$aThis graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field K. The text collects and synthesizes a number of works on Bernstein's theorem of counting solutions of generic systems, ultimately presenting the theorem, commentary, and extensions in a comprehensive and coherent manner. It begins with Bernstein's original theorem expressing solutions of generic systems in terms of the mixed volume of their Newton polytopes, including complete proofs of its recent extension to affine space and some applications to open problems. The text also applies the developed techniques to derive and generalize Kushnirenko's results on Milnor numbers of hypersurface singularities, which has served as a precursor to the development of toric geometry. Ultimately, the book aims to present material in an elementary format, developing all necessary algebraic geometry to provide a truly accessible overview suitable to a second-year graduate students.
001440857 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed November 11, 2021).
001440857 650_0 $$aToric varieties.
001440857 650_0 $$aPolynomials.
001440857 650_6 $$aVariétés toriques.
001440857 650_6 $$aPolynômes.
001440857 655_0 $$aElectronic books.
001440857 77608 $$iPrint version:$$aMondal, Pinaki.$$tHow many zeroes?.$$dCham, Switzerland : Springer, 2021$$z3030751732$$z9783030751739$$w(OCoLC)1245658533
001440857 830_0 $$aCMS/CAIMS books in mathematics ;$$vv. 2.
001440857 852__ $$bebk
001440857 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-75174-6$$zOnline Access$$91397441.1
001440857 909CO $$ooai:library.usi.edu:1440857$$pGLOBAL_SET
001440857 980__ $$aBIB
001440857 980__ $$aEBOOK
001440857 982__ $$aEbook
001440857 983__ $$aOnline
001440857 994__ $$a92$$bISE