Title: Instanton bundles on two Fano threefolds of index 1
Abstract:Abstract We deal with instanton bundles on the product <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>ℙ</m:mi> <m:mn>1</m:mn> </m:msup> <m:mo>×</m:mo> <m:msup> <m:mi>ℙ</...Abstract We deal with instanton bundles on the product <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>ℙ</m:mi> <m:mn>1</m:mn> </m:msup> <m:mo>×</m:mo> <m:msup> <m:mi>ℙ</m:mi> <m:mn>2</m:mn> </m:msup> </m:mrow> </m:math> {\mathbb{P}^{1}\times\mathbb{P}^{2}} and the blow up of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>ℙ</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> {\mathbb{P}^{3}} along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.Read More