Mathematics – Commutative Algebra
Scientific paper
2012-03-20
Mathematics
Commutative Algebra
Research report based on PhD Thesis, Universitat Polit\`ecnica de Catalunya, October 2011. Advisor: Francesc Planas-Vilanova
Scientific paper
In this dissertation, we tackle the problem of describing the equations of the Rees algebra of I for I =(J,y), with J being of linear type. Throughout, such ideals are referred to as ideals of almost-linear type. In Theorem A, we give a full description of the equations of Rees algebras of ideals of the form I = (J,y), with J satisfying an homological vanishing condition. Theorem A permits us to recover and extend well-known results about families of ideals of almost-linear type due to W.V. Vasconcelos, S. Huckaba, N.V. Trung, W. Heinzer and M.-K. Kim, among others. In Theorem B, we prove that the injectivity of a single component of the canonical morphism from the symmetric algebra of I to the Rees algebra of I, propagates downwards, provided I is of almost-linear type. In particular, this result gives a partial answer to a question posed by A.B. Tchernev. Packs of examples are introduced in each section, illustrating the scope and applications of each of the results presented. The author also gives a collection of computations and examples which motivate ongoing and future research.
No associations
LandOfFree
The equations of Rees algebras of ideals of almost-linear type does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The equations of Rees algebras of ideals of almost-linear type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The equations of Rees algebras of ideals of almost-linear type will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-495306