Project Details
Description
First part which is the main one in this project is to study "Effective bound in the three dimensional Sarkisov Program". Every birational map between two given Mori fiber spaces can be factorized into finitely many Sarkisov links due to Hacon, Mckernan and Corti. However, the effective bound to three dimensional Sarkisov program is still open. I would like to give a suitable effective bound of Sarkisov program in dimension $3$ and study three dimensional flips. Second part is to give an appropriate upper bound of the dimension of the ant卜canonical system $|-K_X|$ for all Fano threefolds with canonical singularities. We would like to study the Seshadri constant of $\mathbb{Q}-$Cartier divisor $-K_X$ at the singularities while the degree is relatively big. Another approach is to apply Prokhorov's MMP process and study properties of the anti-pluricanonical map that is related to freeness part of Fujita conjecture. I would like to try to deal this project in picard number 2 case.
Status | Finished |
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Effective start/end date | 1/08/15 → 31/07/16 |
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