论文信息 - No full exceptional collections on non-split Brauer--Severi varieties of dimension $\leq 3$

No full exceptional collections on non-split Brauer--Severi varieties of dimension $\leq 3$

In an earlier paper we showed that non-split Brauer--Severi curves do not admit full strong exceptional collections. In the present note we extend this observation and prove that there cannot exist full exceptional collections on non-split Brauer--Severi varieties of dimension $\leq 3$.

Savsa Novakovi'c

[1] Benjamin Antieau. Twisted Derived Equivalences for Affine Schemes , 2013, 1311.2332.

[2] Savsa Novakovi'c. Tilting objects on some global quotient stacks , 2015, 1503.00522.

[3] Savsa Novakovi'c. Absolutely split locally free sheaves on proper $k$-schemes and Brauer--Severi varieties , 2015, 1501.00859.

[4] A. Kuznetsov. Semiorthogonal decompositions in algebraic geometry , 2014, 1404.3143.

[5] Mark Blunk. A Derived Equivalence for some Twisted Projective Homogeneous Varieties , 2012, 1204.0537.

[6] A. Polishchuk. Simple Helices on Fano Threefolds , 2007, Canadian mathematical bulletin.

[7] Daniel Huybrechts,et al. Fourier-Mukai transforms in algebraic geometry , 2006 .

[8] M. Bernardara. A semiorthogonal decomposition for Brauer–Severi schemes , 2005, math/0511497.

[9] M. Bergh,et al. Generators and representability of functors in commutative and noncommutative geometry , 2002, math/0204218.

[10] D. Orlov,et al. Exceptional Sheaves on del Pezzo Surfaces , 1995 .

[11] A. Bondal,et al. HOMOLOGICAL PROPERTIES OF ASSOCIATIVE ALGEBRAS: THE METHOD OF HELICES , 1994 .

[12] D. Nogin. SPIRALS OF PERIOD FOUR AND EQUATIONS OF MARKOV TYPE , 1991 .

[13] A. Gorodentsev. Helices and Vector Bundles: Seminaire Rudakov: Exceptional Objects and Mutations in Derived Categories , 1990 .

[14] A. Rudakov,et al. Exceptional vector bundles on projective spaces , 1987 .