Tunneling Estimates And Approximate Controllability For Hypoelliptic Equations
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A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria by Jean-François Chassagneux,Dan Crisan,François Delarue Pdf
Peter M. Luthy,Hrvoje Šikić,Fernando Soria,Guido L. Weiss,Edward N. Wilson
Author : Peter M. Luthy,Hrvoje Šikić,Fernando Soria,Guido L. Weiss,Edward N. Wilson Publisher : American Mathematical Society Page : 168 pages File Size : 47,9 Mb Release : 2022-11-10 Category : Mathematics ISBN : 9781470453749
This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses. So it is a suitable text for a beginning graduate course or an advanced undergraduate course. The book begins with a study of plane algebraic curves, then introduces affine and projective varieties, going on to dimension and constructibility. $mathcal{O}$-modules (quasicoherent sheaves) are defined without reference to sheaf theory, and their cohomology is defined axiomatically. The Riemann-Roch Theorem for curves is proved using projection to the projective line. Some of the points that aren't always treated in beginning courses are Hensel's Lemma, Chevalley's Finiteness Theorem, and the Birkhoff-Grothendieck Theorem. The book contains extensive discussions of finite group actions, lines in $mathbb{P}^3$, and double planes, and it ends with applications of the Riemann-Roch Theorem.