Exceptional Bases of Rank 4 Mukai Latices

Student: Nikitin Ivan

Educational Programme: Mathematics (Master)

Year of Graduation: 2017

In this work we give an overview of semi-orthogonal linear algebra, and semi-orthogonal decompositions in derived categories of coherent sheaves, formulate open questions and conjectures, basically, on behavior of the exceptional vector collections under the action of a group spanned by mutations of the exceptional bases,trying to give a partial answers to it, compute a group of isometries of indecomposable Mukai lattice with bilinear form of type .

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