1. Remarks on Type III Unprojection.
- Author
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Papadakis, StavrosArgyrios
- Subjects
- *
GEOMETRY , *THREEFOLDS (Algebraic geometry) , *ALGEBRAIC varieties , *ALGEBRAIC geometry , *GORENSTEIN rings , *NOETHERIAN rings , *ALGEBRA - Abstract
Type III unprojection plays a very important role in the birational geometry of Fano threefolds (cf. Corti et al., 2000; Reid, 2000). According to Reid (2000, p. 43), it was first introduced by A. Corti on his calculations of Fano threefolds of genus 6 and 7. It seems that at present a general definition of Type III unprojection is still missing. After proving some general facts about residual ideals in Section 2, we propose a definition for the generic Type III unprojection (Definition 3.3), and prove in Theorem 3.5 that it gives a Gorenstein ring. Communicated by W. Bruns [ABSTRACT FROM AUTHOR]
- Published
- 2006
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