Qualitative theory of ordinary differential equations: integrability, periodic orb...
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On defective Veronese varieties and the Alexander-Hirschowitz theorem
Full text
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| Author(s): |
Lucas Mioranci
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2019-07-03 |
| Examining board members: |
Daniel Levcovitz;
Herivelto Martins Borges Filho;
Eduardo Tengan;
Israel Vainsencher
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| Advisor: | Daniel Levcovitz |
| Abstract | |
This dissertation deals with the problem of determining all defective Veronese varieties by presenting proof of the non-defective cases. We work on the equivalent formulation which says that, except for a small list of exceptions, k double points on Pn impose independent conditions on homogeneous polynomials of degree d, as proved by J. Alexander and A. Hirschowitz in 1995. Our main reference is the paper by M. Brambilla and G. Ottaviani, and we included a few more details on secant varieties and the relation to the Waring problem for polynomials. (AU) | |
| FAPESP's process: | 18/26163-7 - An introduction to enumerative geometry |
| Grantee: | Lucas Mioranci |
| Support Opportunities: | Scholarships in Brazil - Master |