How Many Zeroes?

Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity

Häftad, Engelska, 2022

AvPinaki Mondal

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This 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.

Produktinformation

Utgivningsdatum2022-11-07
Mått155 x 235 x undefined mm
FormatHäftad
SpråkEngelska
SerieCMS/CAIMS Books in Mathematics
Antal sidor352
FörlagSpringer Nature Switzerland AG
ISBN9783030751760

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Matematik inom Naturvetenskap och teknik

Pinaki Mondal studied at Khulna St. Joseph's School, Barisal Cadet College, University of Saskatchewan and University of Toronto. After a postdoctoral fellowship at the Weizmann Institute and teaching at the University of The Bahamas, he is back in Toronto doing quantitative finance. When not working to safeguard Canadian economy from a collapse, he still makes time to think about algebraic geometry.

Introduction.- 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.