Let M be a moduli scheme of stable sheaves with fixed Chern classes on an Enriques surface or a hyper-elliptic surface. If its expected dimension is 7 or more, then M admits only canonical singularities. Moreover, if M is compact, then its Kodaira dimension is zero.
Let H and H ′ be two ample line bundles over a nonsingular projective surface X, and M (H) (resp. M (H ′ )) the coarse moduli scheme of H-semistable (resp. H ′ -semistable) sheaves of fixed type (r = 2, c 1 , c 2 ). In a moduli-theoretic way that comes from elementary transforms, we connect M (H) and M (H ′ ) by a sequence of blowing-ups when walls separating H and H ′ are not necessarily good.As an application, we also consider the polarization change problem of Donaldson polynomials.
Abstract. Let H and H′ be two ample line bundles over a smooth projective surface X, and M (H) (resp. M (H ′ )) the coarse moduli scheme of H-semistable (resp. H ′ -semistable) sheaves of fixed type (r, c 1 , c 2 ). We construct a sequence of blowing-ups which describes how M (H) differs from M (H ′ ) not only when r = 2 but also when r is arbitrary. Means we here utilize are elementary transforms and the notion of a sheaf with flag.
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 κ(X) ≥ 1, 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.
We present a case of small bowel obstruction secondary to an incarcerated hernia through a peritoneal tear after a laparoscopic transabdominal preperitoneal (TAPP) inguinal hernia repair. A 77-year-old man underwent TAPP repair for bilateral inguinal hernias and developed small bowel obstruction on postoperative day 4. Computed tomography revealed intestinal herniation into the extraperitoneal space at the site of the right TAPP repair. An exploratory laparoscopy was performed and showed that approximately 50 cm of the small bowel had herniated into the preperitoneal and prevesical space through a peritoneal tear in the median edge of the right peritoneal suture performed during the TAPP procedure. The small bowel was reduced, and the peritoneal tear was closed with a suture. TAPP-induced strain/traction on the peritoneal suture line may cause peritoneal tears with a consequent risk of an incarcerated hernia. Thus, careful and firm peritoneal closure is important. Of note, this condition should be considered in the differential diagnoses in patients presenting with such a clinical picture postoperatively.
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