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A celebration of Algebraic Geometry by Brendan Hassett, James McKernan, Jason Starr

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About this book :-
A celebration of Algebraic Geometry written by Brendan Hassett, James McKernan, Jason Starr
This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
The articles gathered in this volume are contributed from many of Joe’s colleagues, postdoctoral mentees and students. The topics reflect the breadth of Joe’s own interests, indeed the breadth of “classical” algebraic geometry in our postclassical era. From all of us whom Joe has led and inspired, we dedicate this volume to Joe as a token of our gratitude.
The conference was funded by the National Science Foundation (DMS-1045217), the Clay Mathematics Institute, and Harvard University. Its success is due in large part to the tireless efforts of Irene Minder and the rest of the staff of the Harvard Mathematics Department. We are grateful to Izzet Coskun for his contributions to the planning of the conference, as well as the other members of the organizing committee (David Ellwood, Benedict Gross, and David Smyth) and the scientific committee (Dan Abramovich, Lucia Caporaso, Kieran O’Grady, and Rahul Pandharipande).

Book Detail :-
Title: A celebration of Algebraic Geometry
Author(s): Brendan Hassett, James McKernan, Jason Starr
Publisher: American Mathematical Society
Series: Clay Mathematics Institute Proceedings
Year: 2013
Pages: 613
Type: PDF
Language: English
ISBN: 0821889834,978-0-8218-8983-1
Country: US
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About Author :-
The author James McKernan (born 1964) is a mathematician, and a professor of mathematics at the University of California, San Diego. He was a professor at MIT from 2007 until 2013.
McKernan was educated at the Campion School, Hornchurch, and Trinity College, Cambridge, before going on to earn his Ph.D. from Harvard University in 1991. His dissertation, On the Hyperplane Sections of a Variety in Projective Space, was supervised by Joe Harris.
McKernan was the joint winner of the Cole Prize in 2009, and joint recipient of the Clay Research Award in 2007. Both honors were received jointly with his colleague Christopher Hacon. He gave an invited talk at the International Congress of Mathematicians in 2010, on the topic of "Algebraic Geometry". He was the joint winner (with Christopher Hacon) of the 2018 Breakthrough Prize in Mathematics.
He was elected as a Fellow of the American Mathematical Society in the 2020 Class, for "contributions to algebraic geometry, in particular his proof of the finite generation of the canonical ring, the existence of flips and the boundedness of varieties of log general type".[7

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Book Contents :-
A celebration of Algebraic Geometry written by Brendan Hassett, James McKernan, Jason Starr cover the following topics.
Classification of 2-Fano manifolds with high index by Carolina Araujo and Ana-Maria Castravet
Abelian varieties associated to Gaussian lattices by Arnaud Beauville
Rank of divisors on graphs: An algebro-geometric analysis by Lucia Caporaso
A tour of stable reduction with applications by Sebastian Casalaina-Martin
The solvable monodromy extension property and varieties of log general type by Sabin Cautis
Effective divisors of moduli spaces of curves and abelian varieties by Dawei Chen, Gavril Farkas, and Ian Morrison
Rational self maps of Calabi-Yau manifolds by Xi Chen
Variations on Nagata’s conjecture by Ciro Ciliberto, Brian Harbourne, Rick Miranda, and Joaquim by Ro´e
Symplectic restriction varieties and geometric branching rules by Izzet Coskun
Riemann-Roch for Deligne-Mumford stacks by Dan Edidin
The regularity of the conductor by David Eisenbud and Bernd Ulrich
Stability of genus five canonical curves by Maksym Fedorchuk and David Ishii Smyth
Restriction of sections for families of abelian varieties by Tom Graber and Jason Michael Starr
Correspondence and cycles spaces: A result comparing their cohomologies by Mark Green and Phillip Griffiths
Geometry of theta divisors—a survey by Samuel Grushevsky and Klaus Hulek
Singular curves and their compactified Jacobians by Jesse Leo Kass
On the G¨ottsche threshold Steven L. Kleiman and Vivek V. Shende, with an appendix by Ilya Tyomkin
Curve counting `a la G¨ottsche by Steven L. Kleiman
Mn¨ev-Sturmfels universality for schemes by Seok Hyeong Lee and Ravi Vakil
Gromov-Witten theory and Noether-Lefschetz theory by Davesh Maulik and Rahul Pandharipande
Numerical Macaulification by Juan Migliore and Uwe Nagel
The non-nef locus in positive characteristic by Mircea Mustat¸˘a
Pairwise incident planes and hyperk¨ahler four-folds by Kieran G. O’Grady
Derived equivalence and non-vanishing loci by Mihnea Popa
Degenerations of rationally connected varieties and PAC fields by Jason Starr
Remarks on curve classes on rationally connected varieties by Claire Voisin


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