
TL;DR
This paper explicitly computes the syzygies of the quadratic Veronese embedding as group representations and constructs sheaf resolutions within the derived category, advancing understanding of these algebraic structures.
Contribution
It provides explicit calculations of syzygies and sheaf resolutions for the quadratic Veronese embedding, a novel detailed representation-theoretic analysis.
Findings
Explicit syzygy descriptions as GL(V) representations
Constructed sheaf resolutions in derived categories
Enhanced understanding of algebraic and geometric properties
Abstract
In this work we explicitly calculate syzygies of quadratic Veronese embedding as representations of the group . Also resolutions of the sheaves are constructed in the category .
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