Flips and variation of moduli schemes of sheaves on a surface
Abstract
Let $H$ be an ample line bundle on a non-singular projective surface $X$, and $M(H)$ the coarse moduli scheme of rank-two $H$-semistable sheaves with fixed Chern classes on $X$. We show that if $H$ changes and passes through walls to get closer to $K_X$, then $M(H)$ undergoes natural flips with respect to canonical divisors. When $X$ is minimal and its Kodaira dimension is positive, this sequence of flips terminates in $M(H_X)$; $H_X$ is an ample line bundle lying so closely to $K_X$ that the canonical divisor of $M(H_X)$ is nef. Remark that so-called Thaddeus-type flips somewhat differ from flips with respect to canonical divisors.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2008
- DOI:
- 10.48550/arXiv.0811.3522
- arXiv:
- arXiv:0811.3522
- Bibcode:
- 2008arXiv0811.3522Y
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14J60;
- 14E05;
- 14D20
- E-Print:
- Revised