Syzygies of adjoint linear series on projective varieties

Guest Speaker: Dr. Purnaprajna Bangere (Purna)

Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. After the pioneering work of Green and Lazarsfeld on curves, numerous attempts have been made to extend some of these results to higher dimensions. It has been proposed that the syzygies of adjoint linear series L=K+mA, with A ample is a natural analogue for higher dimensions to explore. The very ampleness of adjoint linear series is not known for even threefolds. So the question that has been open for many years is the following (Question): If A is base point free and ample, does L satisfy property N_p for m>=n+1+p? Ein and Lazarsfeld proved this when A is very ample in 1991. In a joint work with Justin Lacini, we give a positive answer to the original question above.