Homological and Computational Methods in Commutative Algebra (eBook)

​Aldo Conca received a Ph.D. in mathematics from the University of Essen (Germany) in 1993. Since 2000 he has been a professor of algebra at the University of Genova (Italy). His main research interest lies  in commutative algebra and its interactions with algebraic geometry and combinatorics.  Joseph Gubeladze graduated from Tbilisi State University in 1983. He received his Ph.D. in mathematics in 1985 and Doctor of Science in 1990 from St. Petersburg State University. He worked at Razmadze Mathematical Institute in Tbilisi from 1983. After several research positions in Europe and the USA, he joined San Francisco State University in 2003, where he is currently a professor of mathematics. He is interested in K-theory of toric varieties and lattice polytopes. Tim Römer received his Ph.D. from the University of Essen (Germany) in 2001. Since 2008 he has been a professor of algebra at the University of Osnabrück (Germany). His main research interests are in the area of commutative algebra with applications to algebraic/discrete geometry, algebraic combinatorics and algebraic statistics.

1 Betti sequances over standard graded algebras commutative algebras with two relations.- 2 Betti diagrams with special shapes.- 3 Koszul algebras defined by three relations.- 4 Some algebras with the weak Lefschetz property.- 5 Multigraded gereric initial ideals of determinantal ideals.- 6 A stronger local monomialization theorem.- 7 The Cayley trick for tropical hypersurfaces with a view towards Ricardian economics.- 8 Ideals Associated to poset homomorphisms: a survey.- 9 How to flatten a soccer ball.- 10 The smallest normal edge polytopes with no regular unimodular triangulations.- 11 Homological conjectures and lim Cohen-Macaulay sequences.- 12 Algebras with the Weak Lefschetz Property.- 13 About multiplicities and applications of Bezout numbers.- 14 A polynomial identity via differential operators.- 15 F-threshold, integral closure, convexity.