TAILIEUCHUNG - Báo cáo toán học: "Extensions of Toric Varieties"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Extensions of Toric Varieties. | Extensions of Toric Varieties Mesut ahin Department of Mathematics Cankiri Karatekin University 18100 Cankiri Turkey mesutsahin@ Submitted Dec 24 2010 Accepted Apr 11 2011 Published Apr 21 2011 Mathematics Subject Classifications 14M25 13D40 14M10 13D02 Abstract In this paper we introduce the notion of extension of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property such as being set theoretic complete intersection or arithmetically Cohen-Macaulay Gorenstein and having a Cohen-Macaulay tangent cone or a local ring with non-decreasing Hilbert function from just one single example with the same property verifying Rossi s conjecture for larger classes and extending some results appeared in literature. 1 Introduction Toric varieties are rational algebraic varieties with special combinatorial structures making them objects on the crossroads of different areas such as algebraic statistics dynamical systems hypergeometric differential equations integer programming commutative algebra and algebraic geometry. Affine extensions of a toric curve has been introduced for the first time by Arslan and Mete 2 inspired by Morales work 10 and used to study Rossi s conjecture saying that Gorenstein local rings has non-decreasing Hilbert functions. Later we have studied set-theoretic complete intersection problem for projective extensions motivated by the fact that every projective toric curve is an extension of another lying in one less dimensional projective space 17 . Our purpose here is to emphasize the nice behavior of toric varieties of any dimension this time under the operation of extensions and we hope that this I would like to thank M. Barile M. Morales . Rossi and A. Thoma for their invaluable comments on the preliminary version of the present paper. A part of this paper was written while I was visiting the Abdus Salam International Centre for Theoretical Physics ICTP Trieste .

• Báo cáo khoa học
• báo cáo của tạp chí Department of Mathematic
• tài liệu báo cáo nghiên cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học