Non-normal D-Affine Varieties with Injective Normalization

✍ Scribed by A.G Jones

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 646 KB
• Volume: 173
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1995.1084

✦ Synopsis

Suppose that (\mathscr{X}) is a Cohen-Macaulay monomial variety with injective normalisation the weighted projective space (\mathbb{P}{k}^{r}(m, 1, \ldots, 1)) for (m \geq 1). Then (\mathscr{D}(\mathscr{P}) \stackrel{\mathcal{M}}{\sim}) (\mathscr{D}\left(\mathbb{P}{k}^{r}(m, 1, \ldots, 1)\right)) if and only if (\mathscr{X}) is (\mathscr{D})-affine if and only if (H^{r}(\mathscr{X}, \mathcal{O})=0). We also show that such varieties exist (for (r \geq 2) ) and give a combinatorial condition which precisely specifies them. 1995 Academic Press, lnc.