Birational Geometry of the Moduli Space of Rank 2 Parabolic Vector Bundles on a Rational Curve

Abstract

ABSTRACT. We investigate the birational geometry (in the sense of Mori's program) of the moduli space of rank 2 semistable parabolic vector bundles on a rational curve. We compute the effective cone of the moduli space and show that all birational models obtained by Mori's program are also moduli spaces of parabolic vector bundles with certain parabolic weights.

Mori's Program for the Moduli Space of Conics in Grassmannian

“…Note that there are only few examples of completed Mori's program when the complexity of the moduli space is large. Except toric varieties and moduli spaces with Picard number two (for instance [6,25]), the completed examples are very rare (see [27] for such an example). Theorem 1.1 provides one additional example with Picard number three.…”

Moduli space of irregular rank two parabolic bundles over the Riemann sphere and its compactification

“…The moduli spaces of α-semistable parabolic bundles were constructed in [23], [6], and [9]. The effect on the moduli space of varying the parabolic weights was studied in [11], [5], [25], and [14]. This effect is interesting from the point of view of the birational geometry (in the sense of Mori's program).…”

Positivity of divisors on blown-up projective spaces, II

“…If s ≤ n + 3, X s,(0) is log Fano, hence in particular a Mori dream space (see for example [2,9]). The space X n+3,(0) is of particular interest because it is the moduli space of parabolic vector bundles of rank 2 over P 1 (see [3], [30,28]). The Cox ring X n+3,(0) , end therefore extremal rays of the effective cone of divisors, was given in [9].…”