How Many Zeroes?

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.

“The book will appeal to a reader interested on the arithmetic aspects of some natural intersections and interactions between algebraic and convex geometry.” (Felipe Zaldívar, zbMATH 1483.13001, 2022)