Applications of toric systems on surfaces |
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Authors: | Shizhuo Zhang |
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Institution: | Department of Mathematics, Indiana University, 831 E. Third St., Bloomington, IN 47405, USA |
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Abstract: | In this note we apply the techniques of the toric systems introduced by Hille–Perling to several problems on smooth projective surfaces: We showed that the existence of full exceptional collection of line bundles implies the rationality for small Picard rank surfaces; we proved equivalences of several notions of cyclic strong exceptional collection of line bundles; we also proposed a partial solution to a conjecture on exceptional sheaves on weak del Pezzo surfaces. |
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Keywords: | 14F05 14J26 |
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