Syzygies of quadratic Veronese embedding

Abstract: In this work we explicitly calculate syzygies of quadratic Veronese embedding

m a t h b b P (V) s u b s e t m a t h b b P (o p e r a t o r n a m e {S y m}^{2} V)

as representations of the group

o p e r a t o r n a m e G L (V)

. Also resolutions of the sheaves

m a t h s c r O_{m a t h b b P (V)} (i)

are constructed in the category

D (m a t h b b P (o p e r a t o r n a m e {S y m}^{2} V))

.