Kronos might have some minions do the dirty work for him. They could be disguised as normal people and surround Annabeth when she's alone. Then they could overpower her and take her to Kronos. It's also possible that he uses some sort of magic or spell to immobilize her first and then kidnap her.
One more way Kronos could kidnap Annabeth is by manipulating the environment around her. For instance, he could create a false emergency, like a collapsing building. Annabeth, being the heroic type, would go to help. And that's when Kronos could grab her. He might also use his knowledge of her weaknesses or her relationships to plan the perfect kidnapping.
Percy's reaction could also be one of self - doubt. He may start to question his own actions and leadership. He might think that he has done something wrong to push Annabeth away. However, his loyalty to his friends and the cause would eventually make him stand up against Kronos and try to bring Annabeth back to the right side.
There could also be a situation where Annabeth, out of desperation to save her friends or the world, tries to communicate with Kronos in a more civilized way. She might offer him a deal or try to reason with him. Kronos, being the ancient and power - hungry being he is, would likely be dismissive at first but then start to be intrigued by her boldness and intelligence.
Some fanfictions might explore a plot where Annabeth gets trapped in a time - related situation created by Kronos. She has to navigate through different time periods he has influenced while also trying to find a way to break free and stop his evil plans. This could put her in many dangerous and strange situations where she has to rely on her wits and the knowledge she has of Greek mythology.
One possible motive could be protection. Annabeth might think that there is a threat to Percy that she can only handle by taking him away from the situation. For example, if there's a prophecy that puts Percy in danger and she believes she can keep him safe in a hidden location.
In many fanfictions, Percy might use his water powers in a unique way. Maybe he combines his control over water with his sword fighting skills. He could create a giant water vortex to disorient Kronos and then strike with Riptide while Kronos is off - balance.
Yes, there are likely non - sexual fanfics involving Kronos and Annabeth. Many fanfic writers focus on different aspects of their relationship such as rivalry, power dynamics, or how they interact within the context of the story's universe without delving into sexual content. For example, some might write about how Annabeth strategizes against Kronos in a battle scenario.
One possibility is that her friends, like Percy, would immediately start a rescue mission. They would likely gather all the resources and allies they could find. Maybe they'd consult the Oracle for some clues on where Kronos has taken Annabeth.
In some fanfiction, it could be due to a prophecy. Percy might think that by kidnapping Annabeth, he is fulfilling a part of a prophecy that would ultimately lead to a greater good. He could be trying to keep her away from a certain situation or enemy that the prophecy foretold. However, his way of handling it, which is kidnapping, is a very extreme measure.
Annabeth could also be angry, not at Percy but at the situation or the forces that led to his death. She might vow revenge and start on a journey to find out who or what was responsible for Percy's sacrifice and make them pay. This could lead her into a whole new set of adventures and challenges as she tries to come to terms with her loss.
She might be heartbroken at first. She could try to jog Percy's memory by showing him things that were important to them.